Great welcome digital asset news like a top stories and crypto break them down a bite-sized piece So today welcome to the live stream one of the earlier probably one of the earliest ones we've done Almost in a very long time. So today What we're gonna talk about is exactly or hopefully what is going on for this weekend as we see not only just volatility But different exchanges doing the same thing across the board and it's just uncanny timing So we're gonna take a look at the market if it's holding out, okay, and what's going on I'll also take a look at it's a little on-chain analysis just to see Where people are or not selling and then take a look at market value We'll talk about why the exchange are stopping or slowing down withdrawals and why that is going on now We'll take a look at the warnings from some people such as Arthur Hayes former CEO of bitmex or maybe the current Thing of what's going on with that situation? And then lastly we'll talk about the good news which is few and far between these days, but it is out there So and then of course the very end will do Q&A and I'll answer all your burning questions to the best of my ability So first things first, let's take a look at what's going on with the market They look at some on-chain analysis. So I gotta tell you I gotta tell you for the negativity that is going on in the market and for The different exchanges either halting withdrawals or slowing withdrawals or different crypto companies At risk of being bought out Bargains move surprisingly well. It's a quite uncanny as I say so Bitcoin. I mean it didn't drop a ton That's still at around 19 19 3 the 3m is up a little bit. Everything's just holding in a holding pattern Why is that? Well a lot of these places are in some exchanges to be able to sell or Take your your crypto even off the exchange. You can't do that So this is why things are going on right now, but remember that's not all the exchanges I mean, I believe by and hand still has withdrawals. I believe coin bat coin base still has withdrawals I believe FTX you can still sell and Take your crypto off However for some of these places it's not happening and it makes me wonder exactly what's going on and Which type of entities are keeping their crypto on these certain exchanges? So you can see right here still holding up I mean even Solana and dogecoin is up she be you knew and down the line anything all stellar is down a Point and no one really cares. Let's just tell the holder like me 2.5% for a 7.3% potatoes amazing still on that So that's exactly what's going on with the the market itself again quite surprising. This is what's happening Let me refresh it just to see where we're at freshly Yeah, 0.2% insane so Let's take a look at some quick on-chain analysis just to see where we're at right now. This is from crypto quads Like these guys got some great data and We take a look at first of all, I would like to see First of all, I like to see if the miners are selling and we can't really see it too. Well, let me blow this up I want to go over these What I'm curious about is over the last month or so is If miners are selling off because they had to pay the bills you got to keep the lights on that's just how it is and we saw two peaks here looks like 15th of June and 21st but right now along they continue them looks to be pretty even out Let's let's break that up a year a year You can see there was even even greater outflows or greater cells I mean looking 31st of March when Bitcoin was all those are good days 45,000 Way way higher and of course as it drops down I think this is where they sold a bunch so they can keep the lights on so that's the first part here And we take a look at Bitcoin exchange reserves My question was are people transferring it to the exchanges to sell off Bitcoin so they can cover things Well, not really we take a look what's going on Let me blow this up and that's not to say they won't do this You know later because which market is liquid 24 7365 besides Forex. It's crypto.  Oh and also Monday if you're not from America We have this holiday which we love. It's called 4th of July Declaring independence all that great stuff shoot off fireworks and everybody has a good time grilling out drinking Time with family also what we don't do is we don't really do a lot of trading and the again stock market isn't open So you can't it's things just become Just solid and then a holding pattern So it's a three-day weekend where you don't have access to liquidity in traditional markets But you do have it over on crypto and I just find it the timing quite odd So anyhow about the reserves if we can take it again, let me blow this up over the last month or so We've seen in actuality We've seen quite a drop of Bitcoin being put on the exchanges the blue line here is exchange reserve Meaning that people are taking Bitcoin off of the exchanges. There was a little bit of a bump 13th of June 14th and 15th, and then just sideways Sideways and now here we on as of yesterday the 1st of July. That doesn't seem like it's too much So we'll see how it goes and then over the over the weekend if they're in exchange There's a little bit of an uptick not Amazingly amount Bitcoin taker buy volume people are buying up as things go down as far as the price You can see there's a big buy wall, but I think that's going to dry up at some point and here's the interesting part again leverage Leverage leverage. I just don't get it Why people are going on leverage and I know people will say well Rob I made a ton of money on shorting the market. That's I mean, that's what the markets for I just don't see the 25 50 100x and You know betting on money that you don't have but I mean, I'm not a trader So that's all you and then this one is also interesting The market value versus the realized value and we have talked about this to almost ad nauseam and what we talked about is that basically the values And then anything above 3.7 indicates a top anything below one indicates a price bottom and you can see right now pull this up That we are well below one. Does that mean it can't go further? Yeah, I can go way further way down, but if we take a look we've been under this Market value versus realized value since roughly 12th of June where we hit when we went below one to 0.96 that wasn't the price was 20 to 4 Is that a bad price to buy Bitcoin at well in the short term potentially maybe Bitcoin goes at 13k You're like, oh, I bought it at 22k, but maybe in three five ten years, which I have my site set on Maybe this this probably won't be for me a very bad position Again, not financial vice not a financial visor But we've been under this this ratio for quite some time and look how far the price has gone down. I mean look 19,000 to 10 even when it was down here 189 and we have seen this This market value the MVRV ratio go to as low as actually you see Here it is on June thousand June 21st thousand fifteen zero point eight six zero point seven six thousand fifteen I Think it's even gone. Yeah Zero point seven one or zero point seven so even though today We're at a value of zero point eight six doesn't mean it can't fall further just because it goes below one doesn't mean stay Absolutely bottom, but it is interesting timing so that concludes with market value load on chain analysis Let's talk about this Exchange stopping or slowing withdrawals. Why now I think we kind of get it We kind of understand that there's only so many liquidity places You can you can pull money out of and if you're and if you're losing your tail in Traditional markets margin calls things like that you need cash fast. Where do you go? Not a payday loan service You go to the exchanges or you go to crypto and you start taking money out of there and Simon Just asked the question all these bad news had a drop before the long weekend. I'm like, yeah, that's true We just saw Voyager Stop all withdrawals. We just saw crypto.com. They slowed withdrawals We've seen the problems with Celsius for that was before hand and it is just interesting timing and I and and correct me in the Comment section if there's any other exchanges. I'm not aware of right now That have slowed down withdrawals or have stopped them all completely. I know there's one coin flex Something like that. It's done the same thing. So it just is just interesting timing and It just feels like and I even said I think there's something brewing There's something happening in these three days And there was something that People got wind of or they were aware of and they said hey We need to stop or slow down these withdrawals because the big bad's happening now Does that mean that is that is a for sure thing? No And does that mean just because I talk about it that it will actually happen? No, but Time remains we it's only Saturday. Let's see how Sunday and Monday play out and this was This was a tweet from Arthur Hayes and Arthur Hayes former or current CEO of Bitmex had some legal issues But this is this is him Saying some things and if there's anybody who probably has like like an inside bearing of what people are doing It might be this guy since he hung around with a lot of the the big whales or what it was This is what he states by June 30th second quarter ending, which was two days ago The Fed will have enacted a 75 basis points rate hike and begin shrinking its balance sheet July 4th falls in a Monday And as a federal bank knowledge, this is the perfect setup for you another mega crypto dump There are three ingredients in this humble pie risk assets will again rediscover their dislike for tightening us US dollar liquidity Conditions sponsored by the Fed to crypto funds must raise fiat to Satisfy redemption requirements by continuing to sell any liquid crypto asset again Where are you gonna sell it crypto market? And then of course no cash can be deployed until Tuesday July 5th You know that makes me it brings a question to my mind that we're talking about risk on assets We're gonna take a look at NASDAQ Just to see how it all played out I gotta tell you it actually was up almost a point Of course that was yesterday and that's where a lot of the tech stocks and I'm a little more risky Riskier plays and say like an s&p 500. It's okay. That one stays. Okay However in other traditional markets, I think there may be some stocks that may have been down a little bit And maybe again these people are trying to find a way to sell that and then There was a great video This is from George gammon and he talks about and this wasn't even this was on june 23rd And he talks about why the the truth about the crypto crash and why it was going to crash and really just came it comes down to this The Fed has to do Two things they have to control inflation And the best way to control inflation, of course is by raising rates and also there's this thing called a philips curve As unemployment goes up The inflation rate hopefully will go down. So you have to do a lot of a lot of Finangling behind the scenes to get the economy under control. The problem is right now Is that there actually is a pretty strong market and the unemployment rate a lot is bringing up? Yeah, just did this one. I believe it's at 3.6. Yeah, we're at 3.6 Percent which is pretty stable. I mean we had a big spike here in a thing called coronavirus but so far 4 percent It's been 3 points. Well, February 3.8 then it's gone down 3.6 3.6 3.6 And then we'll see what it is in june. So it's getting a little bit tougher. However, we've seen layoffs in the crypto sector We're going to see layoff in the wall street sector. We talked about this two or three days ago and then gammon here Had a pretty good point. He said He said you see this in the hospitality service some people have left their jobs And they've actually lived off the assets and one of those being crypto and he said one of the one of the owners of Local restaurants He was losing a lot of a lot of his labor force because they were just not they didn't have to work and they said Why why are you leaving? And they said this is like, you know a year ago or so and they said well, I did so well in crypto I don't have to work. I'm just gonna take some time off. He said but now They're coming back going hey, can I get my job back? and I think That meme with mcdonald's guy putting the mcdonald's hat on could be actually 100 accurate. So as workers start to come in Then of course, there's only so many work as you can take unemployment rate goes up The Fed claims victory and says ah see we we raise the rates which of course People don't like too much then they get they panic They start to sell off then the price of assets go down crypto starts to crash first Then we start to see a traditional markets and it's just a chain effect and everybody claims a victory Everybody's happy except for the people of course in crypto So I linked that video. It's about 17 Yeah, 12 minutes. You can watch the whole thing. It's fantastic very interesting So I just think right now for this weekend We're gonna see people sell off where they can sell off Hasn't really happened so far yet and it just makes me wonder because we talked about this yesterday. We talked about about Well, this is a video that I did on June 22nd and I just talked about voyager and their Balance sheets and their loans and their assets and we talked about the rules and and again about 10 days ago or so 10 days ago and I just talked about how I like voyager like the people But I can't trust them at this point take your take your crypto off and um it just It's just odd because they they got a loan for For pretty much everything that he loaned out to three arrows capital They got a loan from Alameda research for roughly the same amount So to me, I'm just like well, they're liquid. They still have it there So why they shut down withdrawals unless there's something that somebody knows that will never be privy to They're like we don't we know that there's gonna be a big run for whatever reason. So we're gonna shut off withdrawals again There are exchanges that have not and if you take a look at those The coin bases the finances the FTX's It's just interesting that uh, there are certain ones that have and certain ones that have not so anyhow Uh, we'll see what happens in the next next two days or so I just find it to be very peculiar timing. I just want to bring everybody's attention And maybe if we get past this weekend, maybe there's a little bit brighter horizon And then of course that only means my next point the warnings Uh, we talk about this at nauseam.  So this was a tweet And it's not that that coup coin is like a big exchange, but it is something to note Uh, Q coin is only 300 341 bitcoin on the exchange. It could use to be much bigger. You can see back here in 2021 Uh, there was a lot a lot more and now it just seems like people just they took it off and they're selling So again, if you Have any crypto on any exchanges This might be the time to take it off if you can take it off I will say that I still got 3 of my portfolio in celsius I still got a little percentage, uh on voyager. I didn't take it all off like I told everybody I should have sold those voyager tokens. It just Didn't pull it bigger and that's it. Uh, guess what rob's not perfect rob makes mistakes Probably mistakes a lot actually I think mistakes. It's just i'm human. That's what it is. So Does the warnings want every reminder of that and then let's get into the good news because Is there any good news? There is some good news may not be something that uh, you want to hear but through the lessons of pain There is A little bit of brightness at the end of the tunnel and this was a great video and I linked it's Telling you the description I'll link in the description and this is a gentleman who He used to work during the 2008 Uh major recession when everything I don't know if you were around but that was when Like there was the unemployment rate went high. You saw massive foreclosures of homes people getting kicked out of their homes Lehman brothers Collapsed I mean the whole world economy was pretty much on the brink of collapse And uh, we went through some pretty dark times but During those times towards the end you're going to hear about the mentality and this gentleman lived through it He worked through it and he's going to tell you exactly how he made it through And just the lessons that he learned. I think this is invaluable three minutes. So let me Because at some point you're going to need this information Let me share my screen Tab Let me mute myself. You don't hear me. I was a frontline worker in the 2008 real estate crash I used to wake up at 7 a.m And drive around lake tahoe where i'm from and check on about 10 to 12 properties that were in foreclosure My dad was a real estate broker at the time and he had a direct connection with the bank that owned many foreclosed homes And it was my job as his assistant I was a young guy back then to drive around once a week and check on all the homes I saw things that would blow you away homes so neglected that people were throwing away all of their trash In the living room for months animals living in the trash in nests People so angry about losing their houses that they would leave human waste in the toilets When they left and I would be the one to discover it months later Sometimes I was the first person on an assignment at a new foreclosed house The first one to see it since the previous owners or tenants vacated People would take appliances toilets They would remove the fixtures all because they were so angry that they lost their house Now why am I telling you this story? I'm definitely not saying that the current recession is going to see real estate hit that hard But I can tell you that other asset classes Maybe hit that hard and here's my wisdom I bought a duplex in 2012 at the very bottom of the market and what I want you to know Is how bad the emotional sentiment was at the time the seller who I bought my duplex from Was so sure that real estate was going to zero that she was crying Tears of joy when I took the keys from her true story The key during a recession is to look for distressed assets whose fundamentals haven't changed The reason I did so well over the years on that duplex investment is because the fundamentals of real estate haven't changed You're going to see stocks and crypto and houses get completely obliterated in this recession And the way to make money is to look at the fundamentals tune out the emotions I just told you that the seller of that duplex was crying tears of joy to sell her property to me at the bottom There are going to be waves of emotions that dominate the markets over the next Two to four years and your job is to find asset classes with the strongest negative emotions But which still have normal fundamentals and which are basically on sale You'll see a lot of tick tockers and influencers say that there's going to be more millionaires made in the next two years than ever before But nobody's telling you exactly how that's going to happen And I just told you the other advice that I have is to look for unique opportunities That are right under your nose that other people might not be seeing because they're not a plumber Or an electrician or whatever you are and you're seeing Opportunities to start businesses or buy distressed properties Or you have special information on a stock or a company that other people don't have because you work in the industry So that Sage advice. So I mean, look, this is what's going to happen I saw it before I'm probably going to see it again exactly what this gentleman has talked about You're going to see people who are really you think capitulation is bad now Wait for a year or so when the official recession numbers come out, which I still believe when a recession I could be wrong But says if this If this isn't a recession sweet, baby Jesus, I don't want to feel one. So this is uh, again Pretty good advice. You're going to see this later on coming down and people are going to Again, this the the same thing happened in uh in 2018 When people could not get rid of crypto fast enough like just get rid of this junk And then of course I went down and down and down and then people were like just happy Just to get it off and I think the same thing is happening now And I think this is one of the reasons why some of these exchanges said hey People are selling and of course, it's not the ideal. This isn't what we signed up for But I think this is one part of the reason so It's time moves on take a look for these signs because it's going to happen again The four worst words in any kind of financial situation is this time. It's different It's all the same thing. It's all the cycles rolling over and over again And that's what's up So that's part of it and then to give you a bigger outlook. This was a great That was a great video by jungle link And uh, it's he shared this from just a gentleman who's just This guy if you think I've seen a lot Uh, this guy's probably seen a lot more than I have just look at that face But he's got some pretty sage advice and it's a minute.  Just now we're just more aware of how ridiculous they are because Well, I have access to more of the ridiculousness that's going on So it's all stupid.   So that's it. So look I know this isn't the ideal And and the situation is what it is. So we can cry about it And we can be upset and we can be hurt or we're gonna see it for what it is these are the bad times and On a personal note, this is probably The worst bear market I've seen and we talked about this yesterday Because in the bear market that I went through in 2018 and crypto one or 2019 There we had to deal with these these de-escalating prices and that's one part But on the flip side, we didn't have to deal with our exchanges shutting down We didn't have to deal with our exchange our exchanges going a you can't withdraw I mean coinbase they'd have outages, but it was just outages and that was a technological issue There wasn't a liquidity or a solvency issue So I got to tell you if you're if you make it through this one if you do You will be battle tested to the to the hilt because crypto has never gone through an economic downturn recession The pandemic hit didn't go through that we made it through that one and of course now Insolvency issues and liquidity issues never really went through that Except besides hacks which if you really look at it It's not the same mechanism, but it's the same liquidity issue or insolvency issue money's not there so if you make it through this and you can See the light for where it's at. I think you're gonna be just fine. So that's what we got for the news today so look, I know it Wasn't the news you want to hear but it's uh, I think sometimes the news you need to hear And that's just a reality of what's going on.  Have a great time. I know I'm going to good times ahead, uh, got the grandson for the weekends growing out Maybe a little I have a a chateau Miller latte It's a vintage year or in America. We call it middle light and uh, that'll be the weekend So let me just think about it in the comment section now if you want to stick around We're going to do q&a answer all your questions the best of my abilities and let's get to it chop chop so Uh, freddy Rob, how do we know if this gossip q-coin gossip is really just but it's It's not about because people in the chat already said I can withdraw just fine So I have no problems. I understand that and your exchange You can do that right now But how many exchanges do we have to go through that say hey, no more withdrawals before we say, you know, maybe I should have taken that off maybe I should Do these things like put it on a ledger Or if I don't have a ledger put on metamask and just stick it there because I control those keys Not your not your keys. Not your crypto So, uh, I'm not saying that's that coup coin or ftx or coinbase or Or binance or stopping withdrawals. I'm just saying why leave it on there What it What is the what is the process? What do you get for them for you leaving on on the crypto because you don't control it?  Take the crypto take control of it and you know how to do it If you have problems with that, it's okay. I had problems myself. That's why I made danteachescrypto.com It's 100 free if you go to the website And sign up under module two. Let me show this as soon as it comes up Module two safety I show you how to do all that stuff What's a crypto wallet? What's public and private keys setting up your ledger? That's any ledger live transferring crypto all the stuff you want to know and I break it down into small bite-sized pieces You know a couple minutes here and there. So that's what we got. All right Hope that helps. But it's a good question freddie. Good question Dun dun dun This is good. Dennis says 2008 was glorious if you lived in australia, I bet And then this one rip jill rogan took the jab. So I learned this yesterday That for any kind of any kind of news that is a little bit Out there you should verify it. So again if we talk about If we talk about excuse me The rules everything's a scam until proven otherwise Verify don't trust so this what the the common always gets to is the reason behind it First of all jill rogan didn't die, but you'll hear a lot of you see a lot of fake stories. So that's pretty good I had forgot about that part. All right And let's see dan says this is the youtuber that wouldn't listen to me about voyager and luna can't believe he's still rucking people So let me just say it like this. That's a good good comment and Let me ask you something So I invested in luna Last year and I took a big chunk of it out Not everything and I paid for my house in Puerto Rico And how often out of it? I've been saying take profits along the way Well, did you take profits? if you let it ride the whole time and and stuck in there, that's uh, that's what I was talking about and me I Did that and then I started a dollar cost average again until luna in ron january And I waited all the way up to the end and I lost five figures However, I took much more out beforehand. So not the ideal, but it is what it is and then also about voyager If you use voyager for over the probably the year and a half or so that i've been recommending it um Did you save on some fees for your for your buys and sells? Were you able to gain yield? Did you take that crypto off the exchange or not? So I understand where people are like, well, you recommended this which I did But I also talked about this other part here And I know people are pissed, but that's just the truth What else do I got to do? Do I got to do it for you? I'm just saying So let me know what you think about I'll probably get slaughtered in the comments But uh, that's why I'm here. I show up every day and take the hits Bottom if ftx acquire voyager those voyager tokens might become ftt. That is uh, true There is um, I don't know if there's talks about it. I know block Block five looks like they are going to sell to ftx for 240 million. There's an option on the table. Just saying Uh calico rod no wonder you excelled as a combat medic You were calm as fugue under this immense crypto firestorm it's just because I took my advice. I didn't take it perfectly I Treat everything as a scam I understand. I need to take things off exchanges. I understand that I have to take profits along the way Did I do as did I do it perfectly? No, I did not But I took enough to not be Freak the f out right now and it's a weird thing because When I was talking about taking profits a while back I got a lot of hate like what's the matter. You're not diamond hands. You're weak Paper hands get out of there. You don't know what you're doing. Anyhow And it's just weird. I don't hear that anymore I don't know Neil says uh still waiting for that mindset. It's sorry Crap So here's the thing. Do you want to be a moderator? Say I want to be a moderator and uh, I'll make you a moderator I need to go to the Let me do this Let's start passing out wrenches, baby Ah, there we are I have to I have to go here Real quick This is gonna look kind of weird God is my head that big? Yeah, yes it is All right, so let's see These are funny All right Cardi B Congratulations, let's see You're not a moderator yet tesla. That's crazy What's the time? Diego, thank you What the Sometimes technology Neil, where'd you go? the Talk about sweetcoin I was gonna talk about sweetcoin today But uh, I felt it wasn't appropriate. Yeah, I will tell you about the sweetcoin real quick. Did you guys know that When you download the the app It's free And when you walk you get free sweetcoins and in september 12th those sweetcoins that you Accumulate will be transferred to sweat, which is a cryptocurrency for free So I know people like rob For first of all, they're like, well, what are they tracking? Are they tracking me? Are they tracking my steps? They track the steps. Okay. Well, they do that data Do they sell it? No I just did a deep dive with the the ceo, which I was gonna release today But I might still do it And he said specifically in our light paper in our terms and conditions and I'm gonna tell you right here We don't sell that data to anybody But we figure out a way to monetize this and then we do that in a specific way Just like on youtube I'm sure you saw an ad before you came on this video They do the same thing on sweat coin and that's one of the revenue services There's also a premium model for 25 bucks a year, which you do not have to pay for it's still free And that's how they do it So like I know when people get pissed off they're like, man, why do you keep talking about sweat coin? Because it's awesome That's why and they don't pay me a dime to to talk to you about it Because I'm like, well shoot if I can get people to walk and exercise Which will help them feel better anyhow on top of that they're going to get free sweat coins And there's going to be an airdrop in september and it's going to be free sweat cryptocurrency tokens What's the problem? So maybe I'm missing something and they're not even selling your data That that's the part that confuses me. So sure Uh Did I miss somebody As I was going on around go mods Yeah, garkin sweatshirt 100 degrees. Well right now it's 745 in the morning Mod me Mod Future millionaire Okay, that's enough mods for today. How about that? We'll go from there if I miss somebody I'll get you next time. Hey remind me a favor. I forget things remind me when we do this next time go Hey, so you're gonna do some more mods that would help out. Okay, let's see Uh, I watch it all 90% of the youtube videos are youtubers in short positions pumping out fud to make more profits in their shorts I've heard the same thing I've heard the same cheese may Which is a gossip that that's uh, exactly what's going on. I don't short But I have heard that from other about other cryptos that are big into trading and I can't verify that so I can't call anybody out Uh, the bone brass had coup coin all to my 0.57 bitcoin withdrawal. However Someone else just said they did the withdrawal and went through just fine again How many exchanges we have to go through before people like I maybe I should custody myself just saying Well, when you own property you still have to pay the government taxes which almost add up to rent The shan's got a great point and that is uh, one of those things. There's like a break-even point between like When you own a house Which to me when you own up own house or houses like we do the only way that it really works out Is if you put an airbnb and a lot of people don't want to do that with their house I don't really me and my wife don't really care because we travel More often than not so when we're not in Puerto Rico or in houston or in past and I'll pass so we're putting those houses out Uh for rent on airbnb so it becomes an asset not a liability. Also. It's great for tax purposes However, you don't remember just like shan says here. There are taxes and there's also maintenance and there's also Utilities and there's also Well repair and stuff like that. So you have to balance all those things out sometimes renting is actually a better option And then a great point butcher and soldier boy If you're not watching the boys on prime great show Pretty bloody and gory. Just so you know, it's not your typical superhero show But it's a good way to keep your mind off stuff and i'm excited to watch The third the third series the third season All right army Devin I trust cavill having a bad news no bad news yet I reach out to the the guys and said hey you got to come on the show Because everybody's freaking the f out about what's going on and you got to we got to talk about this because they don't do Loans which is where I think a lot of people went wrong. They did a lot of uncollateralized loans They also did a lot of defy craziness and that's not where I trust Roth IRA Gets gets their funds of the money from it's from you trading And I think I got to tell you that's why I think you see like a coinbase of binance An fdx up It's because they're you know, mostly a bunch of big trades and they make money on that So that's what they make their money. So you can trade within your Roth IRA account, which is tax-free In your Roth IRA account I don't know if you knew that if you were smart enough to Or if you could see the signs and and start to sell off your crypto within your Roth IRA You can just keep it in cash and that's tax-free as long as you withdraw it at a certain age point depending You seriously my ledger came in the day before Boyd your stop with drills. Sorry If you don't have a ledger also take a look at metamask and people like what about what metamask sucks You still own the private keys, don't you? You still own an amount of phrase which can back that up Just saying Any good series you can recommend the boys is pretty good.  Yeah, I mean we got to do that. We got to do that. I'll I'll do it soon and I'll pass me We could all use a drink, right? Unless you can't drink that's okay There's always good bar food sometimes some of the best wings and such Um, yeah, I'll do that. Love them boys Metamask is not fully self-custody and that's a lot better than uh coinbase or a lot better than the exchanges Paypal's about as safe as you go for an exchange if you can't withdraw yet Yeah, paypal looks to be safer.  I think that's the the safety one, right? Metamask is fully self-custody I mean There have been issues depending on the settings that you apply We've seen that and uh, I believe That was a there's a video I talked about and and there was an issue with Metamask had an issue with being down for a bit because of the difference. What was it called? Different way in which it in which it interacts with the blockchain in your protocol settings, but uh, it's been up so far I'll do a video on that Self-losic says yeah, yeah, it's not so custody. There's some parts about it What about using coinbase? Well, I can't speak to that As long as you have your private keys and your mnemonic phrase that you can back it up sure However, I'm not going to say it because I don't use it and I can I'll tell you what I Think I know Or what I know what I don't know. I don't know a hundred percent on that one Sound off in the comments Richard Hart will save us all and maybe Good question is usd on exchanges covered like a bank us dollars on certain exchanges Are fdic insured not on all of them. So just so you know on voyager It is fdic insured. I believe on gemini also. I want to say coinbase, but uh, check me Don't trust verify But that's only dollars. That's not stable coins. So usdc is not ust is not usdd is not UST unfortunately was not either What about keeping usd on exchanges? I mean you can but look today Can you get your dollars off of voyager? There's your answer Oh, thanks Up to 250k in coinbase And if you would be so kind count Uh, could you link in uh, the uh, the The post or the actual website where it states that again, don't trust verify Please people get educated how all it's working what you're able to remember You can use an old cell phone for cold storage. You know what digital dave over at crazy for cryptos does He has an old computer that is not uh attached to The internet and you can turn it on and off and he just uses that as his cold storage. That's true Something fully offline exactly I hope I didn't make a mistake. I found me about one bitcoin bo. I'll tell you this. I bought one bitcoin at 17 520 17 It was pretty I felt pretty bad when I went to 5000 but Felt like a genius at 30 40 60k And then it drops right down again to 17 6 The thing is is that that's why we always talk about taking profits If you're gonna dollar cost average in you might as well dollar cost average out and then people will always say well Well, why did you keep dollar cost average after the price point? It's just like I think of farming planting seeds If I want to plant seeds at 10,000 And then it goes up to 20,000 Maybe it's like up to 20,000 I go back and say hey, I need some money from the 10k because I just doubled my money You need to you you reap what you sow And then as time goes on that's why I'll always be in crypto because I'll always be investing in different levels and then the parts where I'm Actually need to take profits and should take profits. I can always go back and go. Oh Those those buys I had a year ago two years ago or five years ago. It's time to Time to uh Do little farming not yield farming, but actually reap out or take out what I actually put in That's it let's see Trick tips I don't know about that one That is not true, but I appreciate it There's a lot of smart people in the space It's just that I just try to show up every day and just tell you this I tried to give you both sides of this of a story And like we talked about the crappy part, right? And what could potentially happen this weekend, but I also showed you A little bit of the over the good side about what to expect especially as we start to slip into that Recession by people who've already been there. So I try to keep as balanced as possible I don't want to hit you over the head constantly with with crappy news because you know Then of course I find it disingenuous to just to do it's bad. It's bad. It's bad Without showing you now the thumbnails and the title may not be the most positive because it's kind of hard to do things At once in a thumbnail, but in the video Hopefully I give you a little bit of uh a little hope not hope you um a little hope But also a big fat dose of reality Yeah Bikram we got four days bank holidays could be a lot of price manipulation a long weekend True So what are we doing here? Why are we talking? Let's get out Let's go enjoy the day like you guys got a lot of stuff to do. So do I and uh it involves Playing a little ball. Look, that's it for today. So, uh, if you like today's video give a thumbs up give it a like comments Subscribe all that great stuff. I'll be here tomorrow Anyhow, thanks for showing up. I appreciate it. I'll see you guys. Uh mañana adios


Hello, this is David D. Hernandez, and I want to take this moment to wish you a Merry Christmas. I want you to know I appreciate your prayer. I appreciate your support. I appreciate when you share our content, when you view our content. And I'm so glad to know that this ministry is blessing people all around the world. So I just want to take this quick moment to tell you I appreciate you. I love you. I'm praying for you and Merry Christmas. Thank you for watching EncounterTV. Don't forget to subscribe. Also, help me win souls by spreading the gospel through events and media. Make a one-time donation or become a monthly supporter by clicking on the donate link now.


Hello, and welcome back to the Berkeley at Home Variety Show. I'm Patrick Holmes, and on this week's episode, we'll see how cohabitating musicians are creating and performing new work during the pandemic. We'll talk to a staff member who turns fabric into art, and hear from another staff member who has captured the emotions of shelter in place on canvas. But first, we'll hear from a cow swimmer who is making waves in and out of the pool. Reese Whitley is a nine-time All-American, a five-time Pac-12 conference champion, and a 2021 Olympic prospect. I had the opportunity to speak with Reese about the work that he is doing to advocate for the end of racial injustice. You had mentioned on social media that you didn't initially speak up following the death of George Floyd. I'm curious what kind of made you inclined to speak out when you did? Since all of this has happened, I was in a really low place emotionally at first, and I had a lot of things to say, but I didn't quite know how to say it. So quite honestly, I took a long time just writing in my notes, developing my own thoughts, talking to friends, like, not even really talking to friends, just very close people like my family. And then I finally felt where I was at a point where I was comfortable speaking up about how I was feeling and offering my take on the situation because in the swim space, one of the few black men who is, I guess, visible in the sport, and I felt like a lot of people were wondering what my opinion was on everything that had happened. So it was good for me to kind of release something that was a little heavy, but I'm a lot healthier mentally now for it. So I'm very thankful. Many of the swimming world, I know that USA Swimming had put out a statement initially that you didn't really feel was adequate. What about that did you think was missing and, you know, how did that change when they kind of put out an additional statement?  And yeah, I felt neglected. You know, USA Swimming has a lot of black talent that may not be as, you know, popular as, say, the Michaels and the Ryan's of the world, but still, like, some unmanual is probably one of the most visible Olympians that we have. And they're countless of others who are on that path to being at that level. So it was really disappointing to see a great organization with hardworking people make a statement that I didn't really agree with. But they were so willing to listen, led by President Henshey, great leader, has been so open-minded in this whole process. And unfortunately, I've been able to work with USA Swimming and other black athletes at the top tier level in our sport to make sustainable change for the organization. I'm going to put links to some of the articles that Reese has been featured in down below this video. Staff members from across the UC Berkeley library have put together a compilation of photos, essays, illustrations, song lyrics, poetry, and video. They created this informal publication, Stand Up and Say Something, to inspire organizational awareness and empathy for our communities of color and allies, and as a call to action. When my colleague Jean Smith is not at work, she can often be found manipulating fabric into beautiful works of art. I asked her to give us a virtual peek into the world of quilting. I have been quilting about 23 years now. Yeah, there's many different styles of quilting. First, are you using your sewing machine or are you piecing by hand? If you're doing it by hand, chances are you're doing something called English paper piecing. And it's pretty much just putting your fabric around a little cardboard shape and sewing them together, kind of like that. And then what you wind up with when you're done, and I've got this block about halfway done, is something like this. So that's English paper piecing. But then you can use your sewing machine, do something like that. There are art quilters whose works very artsy. There are very traditional quilters who use reproduction fabrics from Civil War era. So I mean, there's a million and one ways to go about the hobby. And there's usually a niche for everyone. The best advice I have for a new quilter or someone who's interested in it is, if you can, take a beginning quilting class. And also, if you really get hooked by a good quality sewing machine, doesn't have to be computerized. As a matter of fact, I do not quilt. I don't do my piecing on a computerized machine. And it's just another thing that can break. But yeah, the beginning class and having good equipment. You need good scissors. You need a rotary cutter and a mat to cut your fabric. And you need a sewing machine. And that's really it. The rest is just icing on the cake. Another staff member has been expressing himself through a very different kind of art. Matthew Sun is a web designer and web project coordinator in Student Affairs Communications. I asked him to tell us about this diptych he aptly titled 19. During this time, like many of us, I feel fearful, oppressed, and occasionally hopeful. Sometimes one after another, sometimes all at once. These emotions are finding their way into my paintings. One of the projects from my workshop was to make a pair of small paintings, a diptych. I created double portraits of a masculine man and a woman, alert, vigilant, but had fear for it, resolute. I hope that this small diptych, Titan 19, will give viewers a sense of fellowship and fortify our resilience. Thank you. A few weeks ago, we asked you to identify various bare statues on campus. Congratulations to our two first place winners, Nancy McKinney of University Development and Alumni Relations and James Dudek of People and Culture both earned perfect scores. The Berkeley Art Museum and Pacific Film Archive has launched a new series called Duets and Social Distance. These short videos feature cohabitating musician couples who are creating and performing new work during the pandemic. I'll leave you with a sampling of those videos. Thank you for watching and we'll see you again soon. So how can there be overlords when everything is God?


So that, they're like my writing, it's a good day. This is actually oat bran and I chose that because it's actually higher in fiber and there's probably more nutrients because it's all the good stuff from the oats, berries, maple syrup and flax seeds for omega three. Don't need fish. We finally got everyone in the same room at once, eh? So this is the office that is based in London that I'll be working out of and we have the team here. We've got Max behind the camera. My favorite quote that's been helping me a lot is don't let perfect be the enemy of good because that was my problem before and I was stressing out trying to make little insignificant differences that don't actually matter in the larger context hold back my productivity that your environment is the most determining factor for everything. Addiction, if you've got drugs around you, you're gonna use them. If you've got computers and work around you, you're gonna work harder.    As this is over. It's disconnected. This serial killer's talking about eating people and he doesn't have any empathy and it's crazy because the way that someone can do something so evil without having any remorse is like, I've driven a little diagram here, but just to say this is your emotion here and this is your conscience or your mind or it's disconnected from the heart here. And this is where this man here prefers to live. That's why he has no remorse because he's learned to disconnect his conscience, his mind from his emotion. And when you align these two, which is what I did when I got out of the gangs, I started to align my conscience and my emotion. This is where veganism is. This is where empathy is. There's a massive disconnect from people eating animal products and the way they do that is by blocking it out then don't look at the slaughter footage.  So disconnect is huge. This is how people can do such evil things through their secondhand behavior. Getting concepts into action because talking about stuff is good, but having the courage to go and do it is how you make an impact. We should go see what the public think about this. Let's go do some interviews. Oh, dude, where from? From Instagram, right? Oh, Instagram, okay. What's your name? Katya. Oh, me, Katya. Are you a vegan? Yeah. Vegetarian, vegan, vegetarian buffet. Eight pounds all you can eat. Looks good. Oh, my God, look at you. Hello, what's your name? Wanna interview? What's your name? I'm Joey.  Bang, that's how easy it is. Prime someone with an analogy that they understand is wrong and then bring animals into it and... All right, let's go see someone else. Vegan available. There's definitely some flesh burgers going on here. From the 90s, a serial killer, and he got caught for killing people and eating them. Yeah. What do you think about that? Really good. Really good? I love to do that. You love to do that? If they were to see animals being killed, they would react differently to someone who has sort of connected and conditioned to the slaughter process. I think absolutely. I mean, first of all, it's a pretty gruesome process, in all honesty. It's quite gross. It's messy, and then... They struggle a lot? Hey, brother, how are you? Yeah, I'm good, sorry to bust in. Oh, sorry. What's this for? I'm a YouTube channel. Okay. You haven't cleared it with anyone here, though, have you? Oh, are you the boss here? Yeah, yeah. Oh, no, here you go. I'm sorry. Oh, no, that's all right. I need you to delete everything that's been done so far. Almost in two complete minds. So in one mind, when I talked about the serial killer, he was like, yeah, that's, you know, morally wrong, but then he started, he actually tried to start justifying the serial killer's behavior. I mean, he seemed like he was just as disconnected, to be honest. He could clearly separate these two almost identical situations completely. I was trying this whole time to try to help him connect Arthur's situation with his situation. He just didn't pick up what I was putting down. I know you, actually. You know me? I'm a vegan there. Yeah. Oh, damn.  Are you a vegan? Yeah, yeah. What's your name? Someone tried to take our memory card before. I did one. Yeah, someone tried to steal our camera before. They weren't happy about our questions. Oh, my God. That's awful. Oh, good luck. Oh, no, that's all right. I need you to delete everything that's been done so far. So the hardest part of this job is actually asking people for interviews. But once you get in the flow of it, it's all good. Just know, most people will say no to you. Okay, we'll just try these people here. Oh, my God. You want to be an interviewer? Quick? No? You've got to be used to rejection in this game. And I'm very used to it. Don't you worry. Me feel bad.  No, no, the other one. You've got to see what's on his neck. I don't get what, who's neck? Look at his neck. Vegan. You busted me. Yeah, I'm a vegan. No. See you later. Did I give you a card? This is my YouTube channel, so check it out. That's talking to you. That was the best one, yeah. She just ate a burger and she just made the connection. And hopefully she goes vegan from that. Maybe she will. Yeah, it's so funny. They got ethically sourced on the window there. I guarantee they used dairy milk in there, but dairy can never be ethically sourced. It's just inherently abusive and cruel and unseen right to me. There we go. That's the only ethical sourcing. 100% vegan. Let's stop by there. But ain't vegan and ain't ethical. Everything here's vegan? Yep. Everything's vegan. Can I get three of those peanut-baller jelly brownies, please? Are you a vegan? I'm not personally. Have you ever thought about trying a vegan lifestyle?  Ditch milk. Dog-friendly? Also pig-friendly, cow-friendly, chicken-friendly and fish-friendly. All right, let's go home. We're back to the office where I'll sit behind the computer for the next 16 hours. Look at this. Oh my God. Look at that. All right, green grass. Chickens, you know, you're never gonna find chickens like this. And someone's put stop animal cruelty on it. They don't show chickens bleeding out, their heads cut off, feathers being plucked out, guts ripped up on the floor. They just show from farm to plate. There's a bit big here, and that's the disconnect. That's the part that people are disconnected from the slaughterhouse. So what have they got in here? Oh, they've got all Indian stuff, curries, lentils, potatoes. They've got, wait, vegan and vegetarian specialties. Non-vegetarian, so they do serve the flesh of Holocaust victims here on the right. Look at that. I'd rather eat, or do you rather eat severed limbs from a bird that wanted to live? Or some fried onion bargy, some potatoes, and look at that. Onion rings. Or body parts. It's my lunch. Check it out. This here is this oomph. If you can find it, it's called oomph. I nearly forgot. This here, people ask me where I get my V12 from. Right here. This stuff is like gold dust for vegans. Treat it like cocaine. It's very, it's highly addictive. Amazing. Why aren't you vegan yet? You know what? That was the first day everyone was here together, working together. Felt like a team already, eh? You reckon? But like what values are driving the work? You know, what intention is behind that and what outcome we want to see. So the core mission is making an impact in people's lives, helping animals, changing the state of the earth. So I just want that written in as an intention. So it's something we can focus on because big part of the reason I keep driving myself forward is I have an intention every day and I just focus on that and everything seems to work out. Thanks for everything. How do you feel today? I feel kind of strange that I've finally got a group of people together to work instead of just me trying to like, do everything myself. The light's shining down on me from the heavens. Is that the vegan gods? Is that Gary Rofsky? It's the tofu gods saying how happy they are that we're increasing the demand of tofu. That should be the mission statement. Increase the demand of tofu.


What is going on ladies and gentlemen welcome back. I'm rid of the gnaw your host and today we're checking out some more Python tutorials I'm gonna open up idle and we can get to coding Create a new project here. Say this as file dot Python And we will quickly whip out our old Skeleton that we use for every video because we like classes We like object-oriented programming and you know what we like being able to not worry about Importing our modules and that sort of thing. So we have to have these preliminary code And I suppose I don't have to write it out each video, but you know why not It engraves it in my head, that's for sure Okay, and now we are set to go today I want to be talking to you guys about the sum function and that's sum and Usually when you have that built-in function you would just pass in an array. You could have a four five maybe one and then ten And it would return the sum of all the things that are inside that That list or that array or whatever you want to call it and This is a really easy function. I'm sure you can figure it out all by yourself But in case we'll go through a little walk-through and we'll see what we can do here First of all obviously we're gonna need to create a function We can get some we can get some Go on son get some I don't know what I'm saying. Don't listen to me and then here. We'll have the array. We'll pass that in And then for item in the array First of all, let's set an integer variable because we're gonna need to be working with something like that Some equals zero and then some can plus or equal to Some number Because if it's already a keyword, I don't want to bother with that some number plus equal item And we can print and now we don't want to print we want to return That's some I have an error defined. Oh, we do need to do something in this this little constructor here Let's just pass for now So now we can just do actually we don't even need to press we can just run the run the run the function print out self-dot self-dot get some I'm sorry. I shouldn't be giggling at that three four three ten 20 ten again Let's see what we got here get some takes exactly two arguments and seven of them were given Okay, yeah, this has to be an array and run that built-in function some Turn some number. I forgot the name of that variable. It's embarrassing now. We have 50 This works exactly the way we want it to we could add support for some strings if the type of the type of the item is A string we can just convert it item equals The integer form of the item can run that and everything's fine What if we had only some of them we know some of these were strings that should still be okay because It has that same sort of functionality to it. It's just looping through it and seeing if ones that are they'll fix it Not sort of thing So we should be all set. I wonder if the real some function has a support for strings It's worth a try ladies and gentlemen. Don't you think? You can pass an array to it. Let's do a 30 And then 10 and then 10 Let's see what happens. No, we get an error Unsupported operand types for int and string. Yep, it looks like they're trying to do that exact same thing We are just adding to each other with the operands So in our case, we just tried to fix that in case it does pop up for strings So that's all for this tutorial some finding the sum of a list that sort of thing is very easy I know it was a little fundamental but hey the more we know the better and The more we're able to piece these ideas together with for loops and logic and that sort of thing the the more prosperous We will be in the long run. So thank you guys for watching it'd be cool if you could like the video maybe leave me a comment tell me what you think and I'll see you guys in the next tutorial. Bye


Morning, welcome back. So, in the last lecture, we have seen that every 2 by 2 system is linearly equivalent to one of the three types that depends on the eigenvalues of the matrix. If the system matrix has two real and distinct eigenvalues, then the given matrix can be diagonalized and if the matrix is has a real, but double eigenvalue, then it goes to a form of the type lambda 1 0 lambda and the third type corresponds to the complex eigenvalues. And we also had the detailed analysis of the type 1 where the eigenvalues are real and distinct and the system corresponds to what is called the equilibrium point is what is called as naught. And if the eigenvalues lambda mu, the product of the eigenvalues is positive and the product of the eigenvalues lambda mu is negative, then it is called as saddle point equilibrium. And that is an unstable equilibrium. When lambda mu greater than 0 and both the eigenvalues are positive, then the equilibrium point is unstable and if both lambda and mu are negative, then the corresponding equilibrium point is stable. So, that is the type 1 analysis completely. Now, we will quickly go to the type 2 and type 3. So, we will go to the type 2 type. So, type 2. So, the type 2 there are two cases when b 1 is of the form b 1 is equal to lambda 0 0 lambda. This is the case in the type 2. There are two cases namely case 1 case 1 where the eigenvalue is a double eigenvalue, but it has two independent eigenvectors. In this case and of course, lambda not equal to 0, this situation is absolutely no difference. It is exactly like type 1 where you can write down lambda equal to 1 and it is like a node. So, the equilibrium point is a node. Exactly like in the previous here previous class of the type 1 and absolutely no different. It is stable if lambda positive lambda negative. It is unstable if lambda positive. The solution can easily be written as in this case x 1 t is equal to x 0 1 into e power lambda t and x 2 t is equal to x 0 2 e power lambda t same lambda. So, this if you eliminate t you will get x 1 is equal to a constant in the x 2.  So, if you have the phase for trade here you have the origin as an equilibrium point x 1 equal to x 2 is nothing but a straight line. So, if you start any point here and if this is the situation when lambda negative it will be stable. So, it will move along that and it will this is the. So, any point you start it will be completely like this wherever you start the straight line. So, the entire trajectories are given like that it will go. So, that is a phase for trade for lambda less than 0. If lambda greater than 0 I will draw it in the same thing if lambda greater than 0 it is the same thing if you start with, but then it will move away from that. So, this is the for t negative part from here if you start. So, if you start anywhere it will move along this straight line this is the point t negative part. So, it will move along this trailer. So, trajectories are straight lines. So, if you start from here again if you start from this is the starting point and starting point it will go along this trailer. So, you will have unstability this is a phase portrait phase portrait of two systems is not just one for lambda less than 0 you have the complete. So, phase portraits of for lambda greater than 0 you have your unstable thing that is nothing of completely r 2 and for lambda less than 0 it is a completely stable there is no unstability or instability. So, you have the complete e u is equal to the stable subspace and unstable subspace are given like that. So, there is no thing. Now, we will go to the case 2 case 2 in the case 2 if you do again it behaves exactly like the node case. So, there were not real difference between type 2 and type 1 when the real distinct taken values. So, only thing in the type 1 when lambda mu less than 0 it is a saddle point equilibrium that is only difference otherwise it is a node. So, for this case so the b 2 is of this form lambda 1 0 lambda. So, the corresponding system is x 1 dot is equal to lambda x 1 plus x 2 and the x 2 dot is equal to lambda x 2. So, the lambda for x 2 is an independent thing. So, you can solve for you can solve this system separately if you prefer because if x 2 can be solved immediately because it is a decoupled part. Once you find the x 2 you can put it here for x 1 and that is a non homogeneous system for x 1 otherwise you can immediately compute. So, here is an exercise for you to compute now this is an exercise one should do it immediately you for this matrix for diagonal matrix you already know if it is a diagonal entries lambda 1 etcetera lambda n e power the whole thing is the computation of exponential. So, it is a diagonal matrix the diagonal entries will be e power lambda, but how does it look like if for a b 2. So, that is where the exercise. So, you compute your b 2 square b 2 q etcetera and then you compute e power b 2 this computation is easy tell you we are doing this because the computation is not easy for us and also for general matrix does not reveal the trajectory. So, this you can compute to see that e power b 2 is e power lambda 1 1 0 what is this. And, also compute because we are interested in writing the solution you also compute t b 2 t square b 2 square t q b 2 cube etcetera and write down e power t b 2 this is exercise is not hard you just have to do it familiar you get e power t lambda into the matrix will be 1 here t will be here. So, rho will be 1 will be here. So, you can write down now the solution immediately because you can write down the solution. So, your solution will be. So, you can do it either computing e power b 2 or you can directly solve for this system. So, your solution x t will for this system e power t b 2 into x 2. So, if you decouple the difference. So, you will get x 1 t is equal to immediately you can decouple x naught x 0 1. So, you will write down your solution x 0 1 you can do the computation x 0 to the initial values of t e power t lambda x 2 t is equal to x 0 1. Because it is an independent of that. So, x 1 would not come there x 0 2 into e power t lambda. So, you see. So, this will go to plus or minus infinity if lambda positive as t tends to infinity this will go to 0 if lambda less than 0. This is the same case for this also this will go to plus or minus infinity if lambda positive this will go to 0. So, you will have stability if lambda. So, it is again the 0 is called a node it is exactly like that called a node. The only difference is that because of the appearance of this term when you plot the trajectory in the neighborhood it may have a different behavior, but then there is a t here this will go to infinity the effect of x 0 1 will be wiped out. So, you will see so eventually it will be behave like this term because of the t. So, if you plot the solution here. So, for in a typical case if you face portrait if you do if you start here in the neighborhood there will be a twist because of the term like this at all. So, the exercise again is to plot this curves in the properly. So, you may if you start with the trajectory for lambda less than 0 may come if you start with initially there will be some twist it may behave like that it will go to the origin if you start here. So, from here if you start it may. So, it will go to 0 if for the lambda case it will be something like that there may be some trajectory there may be some trajectory difference of twisting because of the neighborhood of the origin there will be, but eventually it will go to the origin. On the other hand for lambda positive if you want to see the lambda positive case the trajectory will be the same, but then it may if you start from here the trajectory may go like this the same behavior s will be there if you studied only thing it will go to infinity it may it depends on the initial values. So, in the neighborhood there may be a motion difference, but eventually either it will go to 0 along a curve given by this x 1 t and x 2 t it is given by the parameter representation x 1 t x 2 t it will go to 0 as lambda less than 0 and it will go to infinity plus infinity or minus infinity from which quadrant you are starting with and the behavior of that one. So, basically it depends on the this here the sign of that. So, it is a case of node. So, the type 2 is exactly the one case of type 1 in the node situation. So, again the equilibrium point in all these situations we call a node and there is a node is stable if lambda positive negative and it is unstable situation unstable if lambda positive. So, that completes the situation of type 2.  So, your exercise will be to compute for this special type of the general matrix it is difficult the matrices we came upon is easy to compute. So, I want you to compute as an exercise e power b 4 that is what our always the job will be e power a and computation will be cos of b minus sin of b it will be sin of b cos of b this is your e power b, but we are interested in e power t b 4. So, you have to compute this one if you compute this one you will get e power t a and matrix will be cos power b t minus sin b t sin b t and cos b t. You can directly compute b 4 b 4 square b 4 cube b etcetera or t b 4 etcetera another way to compute probably this is then may be this is easy to compute you can just try if lambda is equal to a plus i b you can actually see that a power k you have to compute no a not a plus i b you will have b 4 power k will be please check this the validity of this one it will be real part of lambda power k minus imaginary part of lambda power k imaginary part of lambda power k real part of lambda power k that is why you get it cos b if you add it b 4 power of factorial you exactly get cos b t sin b t etcetera you can do it that b 4 of the you have to work with the t b 4. So, correspondingly there will be t here. So, you can do these things exactly yeah. So, with that you can write down your solution now. So, what is the system corresponding to this one corresponding system in y system is y 1 dot is equal to a y 1 minus b y 2 and y 2 dot is equal to b y 1 plus a y 2 and if you write your solution for the system solution y t is equal to e power t b 4 y naught. So, we already come computer e power e power t b 4. So, it will be e power t a into cos b t minus sin b t sin b t cos b t acting upon some y naught. So, you have a representation of the solution. We want to see the phase portrait the aim is to understand the phase portrait. So, let us denote for the time being denote c is this matrix c is the matrix cos b t minus sin b t sin b t cos b t. So, this is the exercise part therefore, your solution y t is in a short form we are at e power t a c y naught where c is this this is a temporary notation. So, what here to understand the phase portrait that is what you have to understand now as t tends to infinity look at these terms here depending on the sign of a depending on the sign of a e power t a will go to plus infinity or minus infinity if a is negative t power t a will go to 0 if a is positive t power a will go to infinity if a is on the other hand what will be this is doing this term cos and sin are periodic with period 2 y cos t and sin t a. So, this shows the second term here when act on y naught shows some rotation because as t tends to infinity these terms this action of this c c y naught if you start with a point y naught it will rotate around the origin that is what c will do. So, c on the action of c on y naught will try to rotate around the origin on the other hand the term t power t a if a not equal to 0 and that will either that is typically the amplitude if a is positive e power t a will go to infinity. So, it will start rotating, but rotation the radius of the rotation will start increasing if a is positive because that is the amplitude if a is negative that will it will go to 0 the amplitude. So, the e power t a will give you the amplitude of the rotation this will give you the periodic rotations around that point. So, we have to distinguish the case two cases when a not equal to 0 and a equal to 0 because when a equal to 0 e power t a will vanish and there is only a pure rotation there is no amplitude change leading to what is called the periodic solution you will would be studying these things in the non-linear analysis more looking for periodic solutions of the trajectory. So, we will consider in this case two cases case with a not equal to 0 of course, recall that of course, b is always not equal to 0 in type 3 because if b equal to 0 then there is no complex part there is no imaginary part the Eigen values are just real and the real case we have already studied. So, of course, b is always not equal to 0 in type 3 because we are in this situation of complex Eigen value. So, we will start with a is a not equal to 0 this leads to a not equal to 0 complex Eigen value. So, we will start with a is a not equal to 0 this leads to four cases according to the sign of cases according to the according to the sign of of a and b. So, what are the four possibilities coming into picture? So, let us try to understand one by one the case one. So, we will have two cases first we brought let us plot the case when a positive when a is positive the amplitudes are increasing. So, if you are starting from any point here it will rotate, but then rotation can take place either it will rotate in such a way that the amplitude should become bigger and bigger in both cases, but the only thing is that whether it will rotate clockwise or anticlockwise. So, there are two options for a positive the rotation can take place in the clockwise direction and the rotation can take place in the anticlockwise case. So, what the exercise I am going to suggest here you try to take if you want to say whether clockwise or anticlockwise what is the sign you have to choose you start with some particular values of b and also particular values of a. So, consider two specific situation choose some b say equal to 1 and choose a equal to 1 and then you take b equal to minus 1 equal to 1 and all that possibilities you try to see that rotation how it take place to see that one specific case if you want to see. So, let us take the case for I want to know that the rotation amplitude is going to infinity. So, what will happen is that if you think that one go. So, one possibility is that it will take an anticlockwise direction and the amplitude will go that is the case. So, your arrow will be something like that the other situation if you take the second amplitude is increasing the clockwise it can go you see it is going to infinity. So, this is your situation with y naught this is the y naught here the only thing is that one will be for b negative one will be for b positive the best way to check is that you consider a specific case for example, with b positive what will happen to that if you want to check here say choose b equal to 1. So, your matrix is cos t minus sin t sin t cos t this is the way you have to look at it and look at see the vector which is starting from 1 0. So, I am choosing a vector from here I am choosing a vector from here or you can see that vector from there it is choosing and what will happen this one this will be suppose I take t equal to 0 that is a situation when t equal to initial point is at the origin. So, when t equal to 0 cos 0 is equal to 1 sin 0 is equal to 0 0. So, it will be 1 0 0 1. So, it will go to 1 0 only at t equal to 0 where it will happen suppose I am taking a rotating pi by 2 at taking t equal to pi by 2 at a later time. When t equal to pi by 2 cos pi by 2 is equal to 0 now sin pi by 2 is equal to minus 1 and sin pi by 2 is equal to minus 1 which I want you to see that that is equal to and this is 1 0 it will move to 0 1 if you compute it. So, what will happen is that if I start from here I will have my situations here this is with if I rotate here next point will be it will take this point y naught if I start y naught from here it will go along this it increases. So, this is the situation with b positive clockwise and this is the situation b negative. Now, this is the case with a positive now you can verify when two more cases will come what are the two cases both these cases are with a negative in this case again the same thing you will get a clockwise rotation you will get a clockwise rotation if you start, but then the amplitudes are reducing. So, it should go towards the origin. So, it will come here in the using. So, this is the situation with b positive then if you start from here if you start from here see it will go to the origin the spirally. So, this is a negative with b negative this is a positive with a negative with b positive. So, to get this you see of course, we are taking a minus b b a that is a matrix we consider certain places you may take this also may be written in the form of a b minus b a, but you have to check the sign properly look for thing. So, the exercise is the best exercise is that take some particular values of a and b with a different all the four combinations and try to focus here. So, and this situation is called focus. So, we will have this is called the focus it is a stable focus in all the situation all these four situation we call the equilibrium point a focus and stable if a negative. So, it is depending on the real part of the Eigen value the stability always depend on the real part of the Eigen value not about the complex part the sign of complex part determine the orientation of the trajectory. So, you have a two focus is unstable in the first situation first two figures and it is stable in the next two figures. So, we have left with one more case with a equal to 0 case now the last case which we want is case with a equal to 0.  So, there it is always come back to if you have the trajectory. So, if you are trying to do a phase portrait here and you have a equilibrium point it will only thing is that it will rotate like this the other situation which you get is that it will rotate like this that is only two possibility again it you have to see that which direction it will see this is the clockwise direction with earlier case we have already seen that. So, you have this situation. So, you have you see this is a b case positive case you have an clockwise and b negative you have only clockwise. So, you have so you have this is the case with the b positive and this is the case b negative such a point here 0 is called a center called a center. So, with a non 0 it is a focus in the complex situation when a equal to 0 it is a center the equilibrium point is called a center completely. So, that giving in 2 by 2 systems we have a complete analysis of this one. So, let me give a fine definition finally consolidating all the results we will write the definition for a 2 by 2 system for a 2 by 2 system any system one system one what is the one system let me recall x dot is equal to A x the equilibrium point the equilibrium point 0 is called one saddle point if lambda mu negative node here that the moment lambda mu is negative it cannot be complex second values. So, it is a automatically it tells you that is second value to a node if lambda mu real here you have to say it is real and lambda mu positive. Lambda mu positive because if lambda mu lambda mu even in the complex case will be real even if lambda and mu are complex because lambda will be a plus i b mu will be a minus i b and hence lambda mu will be a square plus b square. So, it is always positive and it is unstable if lambda positive mu positive stable if lambda negative both the eigen values are negative and third situation the equilibrium point is a focus called a focus if lambda mu complex with real part of lambda both real part of lambda is not equal to 0 because real part of lambda is not equal to 0 and that is also a condition stable if real part of lambda is real part of lambda is negative unstable if real part of lambda is positive the last case for a center if the same thing lambda mu complex with real part of lambda equal to 0. So, you have a in other words purely imaginary that is pure imaginary. So, we have a complete analysis of the 2 by 2 system there is an interesting bifurcation diagram will end this 2 by 2 part before going to high dimension there is a bifurcation diagram nice bifurcation diagram. So, you can get a picture this bifurcation diagram is in the bifurcation diagram this is in determinant trace space determinant trace plate what is what do you mean by that determinant trace plane given a thing you given a matrix you can write determinant of a is nothing, but the product of eigen value let me call it this is to delta by definition and then you call it alpha the trace of a that is nothing, but the sum of eigen values then you know that clearly because this is the product and this is the sum and it solves a second order algebraic equation. So, this would be in the coefficient of the power term. So, the eigen values satisfy the eigen values satisfy the quadratic equation right quadratic equation z square minus alpha z that is the sum of the eigen because it is a roots. So, it is a coefficient of that plus delta equal to 0. So, you can write your lambda mu as solve that equation lambda mu the eigen values can be written in terms of the determinant and the trace that is equal to alpha plus or minus square root of alpha square minus 4 delta by 2 you see. So, you can write your alpha is one is the alpha plus square root of alpha minus 4 delta by 2 and the other one is alpha minus square root of alpha square minus. So, I am going to draw the diagram in the plane determinant by this is alpha that is nothing, but the trace and this is delta delta is equal to lambda mu and this is equal to lambda plus 1. So, this is nothing, but alpha is equal to lambda plus mu. So, what is this? So, let us consider all the cases. So, below this domain below the alpha x is delta. So, this is the region delta less than 0 delta is equal to lambda mu less than 0. So, what is this region? This region is this region the complete region complete negative region on that you have all 4 points for lambda mu satisfy it belongs to this region that means delta less than 0. So, you have your saddle point here. So, you have your saddle you have your saddle point this is the saddle point this region saddle point. Now, let us look at the situation here when this Eigen values are real Eigen value it is real. So, you have lambda mu real if alpha square minus 4 delta greater than or equal to 0. So, you have to consider the equation in complex if alpha square minus 4 delta less than 0. So, in the alpha delta plane alpha square minus 4 delta equal to 0 determines a parabola.  So, you have your parabola here and this is nothing but the region alpha square minus 4 delta equal to 0 and what it shows that. So, you have a different thing this is the region alpha square minus 4 delta positive this is also the region alpha square minus 4 delta positive here is alpha square minus 4 delta negative and here alpha square minus 4 delta negative. So, that gives now you will consider this case again on that case when alpha square minus 4 delta greater than or equal to 0 1 Eigen value here with the plus sign here will remain to be positive. So, 1 of the Eigen values minus that will be negative because alpha square. So, if you look at here alpha square minus 4 delta positive this region if you look at all this region corresponding to this one alpha square minus 4 delta positive you will have the stable focus unstable in this case it will be unstable unstable here is a region with node. So, you have unstable node because it is a situation where you have real Eigen value. So, you have only node here also this is a situation it is a node thing, but then you have the other thing and you will have your stable Eigen value here.  So, this is the situation alpha square minus both are nodes, but here you look at it here it is alpha is equal to with alpha positive and this is the region with this part is the region with this part is the region with alpha negative. So, you will get your Eigen values in this region both Eigen values will be negative in this region we will look at it. Similarly, if you look at here you will get unstable focus unstable focus and you here you will get a stable focus. So, you have to understand that this is a region this entire region is where delta is equal to lambda mu positive.  What about this here this region this line on that line you will see that the real part is 0 the real part is 0. So, that is the region where you have center you see. So, this is the region.  So, this portion the first quadrant first quadrant is the unstable situation quadrant of course, the third and fourth are already unstable because of this added point equilibrium the first quadrant is unstable unstable and this is called end is called the end is called the source and second quadrant is stable called part this is called the sink see everything will sink there. So, this gives you a complete you do not have to think in a determinant press plane you can completely understand where your stability and instability is happening where it is added point where it is not where it is focus where it is thing.  So, we will now try to give some interesting 1 or 2 examples and before going to higher dimensional situation. So, we will at least give 2 examples. So, here is an example 1 we will have more examples later example 1 example is a situation where your eigen values previous thing there is one more thing what you where is the picture. This is the situation this case let me have a different color this is the case where you have the degeneracy you see this is the situation where determinant is 0 which is a kind of degenerate situation is a degenerate you will have the degenerate case that is a region that is what we skipped. So, that is a we will see an example of the next one. So, consider an example with a matrix a is equal to 0 0 0 minus 2. So, what are the eigen values eigen values are lambda equal to 0 and mu equal to minus 2. So, we want to determine of course, x equal to 0 for any linear system the origin is an equilibrium point, but if a is invertible origin is the only the equilibrium point because the equilibrium points are given by a x equal to 0 set of all x such that a x equal to 0. So, if invertible only x equal to 0 is the solution to that one, but here is a case determinant of a not equal to 0 this is a case determinant of a equal to 0. So, you have to look for what are all a x equal to 0 you want to find all the equilibrium point a x equal to 0 immediately will give you x the second component this is x 1 x 2 the second component is 0 that is all you give first component it does not give you anything because the equation say x equal to 0 is equivalent to 0 x 1 plus 0 x 2 is equal to 0 second one is 0 x 1 minus 2 x 2 equal to 0. So, that show x 2 equal to 0 that mean every point on the x axis the x 1 axis every point on the x 1 axis is an equilibrium point it does not put x equal to 0 does not put any conditions on the first component of x that implies any point every point every point on the x 1 axis is an equilibrium point you see. So, equilibrium is a equilibrium point so now I want to solve this equation. So, what are the equations you do not have a the equation the first equation the is equal to x 1 dot is equal to 0 because say x equal to 0 implies x equal to 0 x 2 dot is equal to minus 2 x 2. So, if you solve this equation you will get x 1 dot is x 1 t is a constant that nothing, but a constant is the initial point and x 2 t is equal to x 0 2 into e power minus 2 t you see. So, what does it shows that now if you are trying to find a this is nothing, but an equation of a line, but it is an equation of a perpendicular line. So, that is why it cannot be written as a function of x 1 variable and anyway x 1 this is x 2. So, what I am trying to say is that every point on this is an equilibrium point all the points are equilibrium point not just the origin all points are equilibrium points and what does it say that. So, if I start a point from here x 0 what does this say that if the first component this x 1 trajectory says that the first component will not change. So, this will be your x 0 1 this will be your x 0 2. So, if you start from here the first component will not change and the second component says that it will go to the same x 0 it will go to the 0 this goes to 0 as t tends to infinity. So, the second component goes to 0 and x component will not change it will remain if it does not change it has to come along this. So, it will move along this. So, whenever you start here the trajectory will move here as t tends to infinity you start from here it will move to that anywhere you start it will go towards that because x 2 component. So, all your trajectories are given like this all whatever your trajectory you start it will move towards that. So, this is the complete phase portrait of this system phase portrait. So, in other words starting from. So, you are starting from x 0 1 x 0 2 at time t x 0 2 at time t x 0 2 at time equal to 0 the trajectory moves to towards moves towards only at infinity moves towards x 0 1 origin along the perpendicular line along the perpendicular line you see the behavior difference in that one. So, we will go to another example how the linear transformation linear equivalence example will change. So, you will start with a system which is not in its normal form. So, you consider a system consider a system let me write down x 1 dot is equal to. So, part of it is an exercise also minus equal to minus x 1 minus 3 x 2 and x 2 dot is equal to your 2 x 2.  So, let me put it in a different color the exercise show that the A Eigen values are clear A Eigen values immediately know A Eigen values are lambda equal to minus 1 mu is equal to 2 with A Eigen vectors find the A Eigen vectors with A Eigen vectors with A Eigen vectors 1 0 minus 1 1. Therefore, the matrix P which converts to a linear equivalent matrix because these are 2 distinct Eigen values.  So, what is a y system therefore, your y system is y dot is equal to A y that is already we have studied it is a standard problem which an saddle point equilibrium now is clear because you have 2 real Eigen values with opposite signs and hence it is a saddle point equilibrium. So, you can write down which we have done already the solutions. So, if you plot this curve here immediately I do not want to go further here to you can do that one. So, if you plot your y this is for the y axis this is your y 1 this is your y 2 and this also says that the first Eigen value the corresponding to the first Eigen value minus 1 and you have a the first component stability the second component stability totally instability, but then it is a saddle point equilibrium you will have this one. So, this is your phase portrait here phase portrait and y 2 go to infinity and y 1 go to 0. So, y 1 go to 0 means your graph will be like this. So, y 1 will go to 0 you see it will go to 0 this will go to 0. So, this is. So, this is where phase portrait of that and it is an invertible matrix. Now, we want to know the solution corresponding to x 1 you can of course, do the analysis because you can write down from here e power a t you can write down a is nothing, but p b p inverse you can write down the solution. And then your solution is you can write down as e power t a is equal to e power p a of x naught is nothing, but p b p inverse of x naught p b p inverse of x naught. So, you choose this p inverse of x naught as y naught. So, this is starting with that p b of y naught and p b you can write down the solution completely immediately. So, the solution is x t is equal to e power t a of x naught is nothing, but p you can completely compute b is the diagonal matrix. So, it will be e power minus t 0 0 e power 2 t of p inverse we already computed. So, this is your solution. So, you have your solution completely you can plot it separately, but then let us try to understand the transformation in this slide itself. So, that we do not need in another way. So, what is your transformation going? So, your transformation y going to x equal to p y this we already discussed. So, you compute that one if you do that transformation how does my axis I told you in the beginning this kind of transformation linear equivalence is the coordinate change. So, I want to know that how does my y 1 coordinate changes. So, I want to first compute p of 1 0 if you compute p of 1 0 you just take p is equal to 1 0 is nothing, but 1 0 itself. So, the y 1 coordinate axis goes to x 1 axis itself, but what I do to my second coordinate axis p of 0 1 the y 2 axis and the y 2 axis you can see that it is minus 1 1 that is what it will go to 0. So, if you plot. So, that if you say if you know try to sketch my in the x 1 x 2 plane the if I sketch the x 1 the y 1 axis go to your x 1 axis. So, I will plot here. So, let me choose a proper color. So, if it is you see it will go to the same color, but then the x 2 axis goes to p 0 1 goes to minus 1 to 1. So, it will go to this axis it that is what the y 1 minus y 2 plane. So, it will go to this plane. So, this is the new coordinates now this is y this is the coordinate y 1 plus y 2 equal to 0 or x 1 plus x 2 equal to 0 you see that is where it goes. So, the y 2 axis actually transform this one. So, now the trajectories do not intersect. So, the trajectory corresponding to this one if you take it will go like this. So, the trajectories will be like this and the corresponding trajectories will be the even the directions will not change it. So, the directions will be like this. So, the trajectory here it will be only so the saddle point equilibrium. So, this will be the trajectories in the. So, that is the trajectories here and this is the trajectories here. So, this will all will be unstable the second component is unstable the first component is stable. So, it is till you get the stability here this will be in this direction you know there is not we are not talking about that. So, this will be here this is direction. So, this is the phase portrait phase portrait of the solution phase portrait of the solution. So, that gives you that is what in the beginning I have told under linear equivalence under this thing the trajectory behavior the equilibrium the stability of the behavior do not change whatever stability you have the you will get the same thing. So, the picture something like will be changed it to transformed into a new coordinate system. So, with this the will stop the complete 2 by 2 part now we will not be able to do such a detailed analysis for the higher dimensional system, but we will appeal to the Jordan decomposition what are the best possible things we can do it in higher dimension. We will begin with one or two examples and possible ideas behind it and then we will see what are the blocks coming in higher dimensional system in the next lecture. Thank you.