So you want to tell him we sold the house come here Frank come here you gotta go around come on go on go around you want to tell him we sold the house and yes I'm wearing shades in the house because we're kicking up a lot of dust apparently and my allergies are attacking me so you know what you know I'm going I'm going puffy eyes and all you can see me the way I am we sold the house that's right did you guess it already did you already know because yesterday I said you're probably gonna piece everything together everything's pretty bare in here we sold the property and we bought new property so this is actually the last couple of days at this place bittersweet happy face and sad face at the same time doesn't work I'm sad that this was our home and we really love it here we don't want to leave but it's a little bit much for just us we had about 17 acres here and there's a lot to take care of I was on the road a lot of time Brits here by herself when I come home it's pretty much just yard work yard work yard work and we don't even have the most fancy yard here I mean we had lots of plans to landscape it and make it even better but just became a little bit too much so we're downsizing we're downsizing into a small 800 and 890 square feet right 86 860 that's right I always flip the six around no it's not actually 890 it's 860 square feet we're moving into a tiny little house and we're going to be saving up to build a house in a few years we've also bought a plot of land outside of town we're not going too far away from here we're still staying around Steinback but that's the plan now downsize and live the minimalist lifestyle for probably about five years maybe a little bit more depends if kids come along or not it's a little two bedroom house that we're moving into so if we had you know more than two kids in the next five years it would still we could still make it work but after that we would definitely have to upsize and we're planning on building that anyway so we'll show you the lot eventually not today and we'll do a house tour when we move in we're moving in next week that's what I need to be home for that's why I had some scheduled time off that's why I'm having a little bit of trouble finding work to do to keep me close to home because I have to make sure that I'm home on moving day which is Monday not this Monday the following Monday it's coming up fast everything happens so quickly we put the host on the market three days later sold how do you feel about it honey tell the tell the YouTube's how you feel it's better sweet I'm going to miss the space and the quiet but I'm happy because it's gonna give us a better future yeah you think we're gonna be okay in the tiny little house you're gone most of the time and I don't mind a little house with just the pups it'll be fine we're excited about it our bills are literally gonna be cut in less than half so we're gonna have a lot of extra spending money well we're actually gonna be saving money saving money saving money it's gonna look a lot better those numbers in our bank account as opposed to what they look like you know when we're living at the top of our budget here mm-hmm so today is the garage sale we've got to get rid of some of ours a lot of most of our stuff we've got donations included we've gone rid of probably like 40% of our stuff and and we still can't fit our stuff into the new little tiny house oh no we're gonna have a ton in storage for years yeah dad's gonna help us out and let us put some stuff in his shop and stuff but until we build we're gonna be living the minimalist lifestyle some of the stuff we're gonna keep like our lawnmower obviously that's very important we're gonna keep that in storage because when we have our bigger lot it's bigger lot that we bought we're gonna have a bigger lawn again not quite as much as this but we're gonna need the mower then so we'll keep that but for today we're doing a combined garage sale with our friends Rick and Sabrina in Steinbach so this garage sale would have happened yesterday for you so if you come out when you watch this we won't be there anymore actually it's a three-day garage sale but I work tomorrow so Sabrina's gonna work it herself because she's a fabulous lady and then Sunday I'll be back because I have Sunday off obviously nothing's open so I'll be there Sunday to work it it's a three-day garage so it's a whole weekend go bigger go home okay well this weekend's our garage sale and we're selling not all of this but her car's already all loaded up we're selling all this I've already bought or bought I've already brought two loads to their place I filled my terrain like I folded down the seats filled up the whole back twice brought it to their place and now we got to bring this and this is just the folding table to put stuff on that's not for sale no heck no I love that thing we don't know where we're gonna put it but it's not for sale our this tiny house literally has no storage it has two bedrooms a laundry room which is also the entryway one bathroom a living room which has room for like one of our coaches but we're gonna try to fit to and a kitchen with room for like a little two-person dining room table yeah like a cafe table yeah I can't wait to give you guys the tour oh I think there's a shelf above the water heater there's a shelf there's a shelf we have a shelf and there are two sheds in the backyard that's true this is a tiny little town walk that we're moving into so we'll talk more about that when we actually move into it because it's I don't want to just explain it just by talking now you gotta you got to see it gotta see it to believe it yeah and there is a carport there but we're probably going to be dismantling that eventually but we'll use it for storage for a little bit we'll see anyways yeah let's uh let's go do some garage sailing it's not a garage sale without Timmy's it's not really a day without him it's lunchtime I came here at the worst possible time this is the Timmy's near the high school and it's lunchtime and school is back in so you know what's going on right now the same thing that I did when I was in high school everybody crowds into Timmy's all the guys crowd into the parking lot rev their engines of their four cylinder civics everybody's trying to get attention and everybody's holding up the line I used to be one of those guys man was I cool tell you what you haven't seen cool till you saw 17 year old trucker Josh that was cool in my Chevy Cavalier still got a Chevy but I've got a man's Chevy now got the Silverado Silverado so I've got a list here from the ladies of what they want I guess I should look at it so I'm not stumbling over my extra large steep tea one milk half sugar a bacon English muffin a honey crueler and medium double-double it's not too hard too hard usually they would send me with a much more difficult list than that so it looks like I'm gonna be home all weekend now we have to sign papers with the lawyers and the banks for our new house on Monday and Tuesday which means I can't go anywhere because I have to be home and sign in person because they need to witness it and it needs to be official and legal and stuff like that so no work again for and I don't even know because I got to be home at the end of next week to pack up and move right so man am I gonna be off for two weeks now I hope not they're gonna try to find me something short to do next week but we're gonna try to entertain ourselves what I mean what do I mean try to we got lots to do we're gonna entertain ourselves at home this weekend go sign some papers early next week and hopefully get on the road and see what happens but none of that matters right now because we're at Tim Hortons and Tim Hortons is all that matters right now we're next in line are you excited I'm excited super duper super duper you're supposed to say awesome paw some back when someone says super duper to you proper etiquette bandit rick and Sabrina's dog hey you got the ball oh no you got to drop it you got to drop it come on okay then we can't play fetch we can't play fetch see oh thank you thank you well oh good boy watch this watch how smart he is you think he knows how to get up there watch this oh it went down the slide come here bandit yeah I want to show him your skills come here throw that up there figured out bandit smart boy you go down the slide good boy he reminds me so much of diesel when diesel was young it's got that same energy look at him no problem straight up the ladder and down the slide my boy diesel was just like you he still is just he's a little bit older now bandit I think is a year-old think he's a year-old right still a little that puppy energy in you got it I mean the guy got that on camera you're so fast good boy so now that the cat's out of the bag and you know that we've sold the house and we're moving now I can share a little bit more with you but what we're doing because everything we're doing in the next week has to do with us moving so now we got the garage sale going on over here the ladies are gonna man the fort or woman the fort and I'm gonna go and reserve a u-hole too little too little too small too small too small there it is there she be that's the one we need to reserve f650 for those of you who are Ford lovers you're gonna be very happy to know that our move is being made possible by Ford which is okay I don't hate Ford Ford's are actually great here's how my love of trucks goes Chevy's up here Ford Dodge that's the way it goes so Ford is okay Ford's second best in my mind but I know a lot of you are big Ford they actually make really good trucks really good vehicles so does dodge they're all great vehicles I just you know you know how it is you got to pick a team and I pick Chevy pick it up on Saturday bring it back Monday after we're done unloading it into the new house man this is coming up fast we've been working on this for quite a while already and we didn't want to jump the gun and reveal everything right but now that it's a week away like whoo this is happening this is happening man we'll have to take you down and show you our our lot that we bought as well now we'll do all that next week as it happens we got to save something to vlog about then right so we've been at the garage sale all day or all afternoon I'm gonna run home real quick to the house let the dogs out and let them stretch their legs run around for a bit and then come back and hang out with the girls at the garage sale for a bit longer lots this all's are shouting prepare yourself okay we'll let you out in a minute where's everybody else oh do you smell bandit on me you smell bandit you should have you sit so exciting so exciting I know guys we only got like a week left in here man it's so sad that we just installed this door and then we sold the house we weren't planning on selling when we installed this we decided that after and the next people will get to enjoy it on everybody diesel be careful he's little I am gonna miss it this is our reward for all the hard garage sale and today true story and for all of you who have been asking here she is she's been here the whole vlog today mm-hmm also a true story true story you saw it not fiction mm-hmm she's still here we're still married oh yeah totally haven't been filming just haven't been filming at home as much and we're gonna change that yes I like this new system that we're doing now keeps the vlogs more relevant and more exciting and it gets you inspired to be a little more creative yeah even a little more excited about vlogging you've kind of lost your passion last few months so yeah I did yeah I went through a rut when you do this every day for years and years and years it's you know it's a rut so I found my creative bone again I feel excited and now we've got an exciting all kinds of exciting stuff going on I mean with the new chapter and now I just found out today I may not even I think I told you already I may not even get a load out until after we move now well we'll see what happens but we're gonna have to sell more stuff at the garage sale yeah we're going back tomorrow and the next day I don't totally pay the bills right guys want any stuff we got lots of stuff we're selling so much stuff we got to take everything that we filled up this whole house and look 1800 square feet some 1900 square feet oh 18 it says 1823 on the ad but last we were told it was 1875 so 18 came either way between 18 and 19 yeah and we have it filled up or we had it filled up and now we got to squeeze all of our life into 860 square feet with zero storage and we told you about the land that we bought we'll take you to see that next week sometime but there's nothing there it's just land we got to get power in there sewer in there we got to build our house beautiful majestic nature walk yeah so we're gonna have exactly the same style of property as this that doesn't have the pines there though that's fine it's all mostly poplars but it'll be same country feel as this except we'll have a brand new house designed exactly for us and that'll be in like five years maybe more but we'll see what happens for now we're moving into this tiny house to save money and to live the minimalist lifestyle and enjoy the convenience of town garbage pickup guard yeah that I'm actually excited about cell phone service yeah the other one pizza delivery yes even though I don't really like any places in Steinbeck that deliver and don't tell me Rathaus is amazing because guys I tried it and maybe it was just a bad day but no fans Rathaus but we have high standards we do we buy the super store pizza they're actually really good six bucks each very good than anything else and way better super store used to have the Chicago deep dish style pizza as well I'm not sure if they still do or not it's like that thick holy smokes mm-hmm so good but I gotta eat some really badly sunburned and I'm feeling a little bit dizzy she got sunburnt today in September in September in the shade 90% of the day but yeah we're really looking forward to it you go ahead and start there and I'll be there right away but we're looking forward to the convenience of town but you know me I'm not looking forward to having neighbors right next door to me and living in a town I'm just that's not me but we do have a plan to build out in the country and build a lot that's there's certain things about this lot that really didn't sit well with us and I was telling you before we had almost 17 acres here and it's so much to take care of we want to make it a little bit more manageable man we'll take you along for the ride we'll talk more about it in the future for now we're gonna eat pizza so thanks for watching today tomorrow's another garage sale and a I hope you tag along with us it's gonna be fun well I'm gonna be at work it's gonna be fun for him oh yeah take care everybody hit that like button ring the bell down there so that you get a notification when tomorrow's vlog was live all of our social media is down below this video if you want to hit those links and follow us anywhere there and other net see you tomorrow


Hi everyone, Joe for jaspyscasewrakes.com coming at you with a one box break hobby edition of 2020-2021 Panini prism basketball. One spot gets you three teams in this one box break. This is Ram team break number two. Big thanks to this gang here for getting in on the action. So let's triple you up here. There's one already. There's two and there's three. And there's all 30 teams right there as well. Let's roll it, randomize it one and a three, four times for names and teams. One, two, three. And once more, fourth and final time. We got Matt. A couple of mats up there down to Steve. Last spot mojo in the last spot. One and a three, four times for the teams. One, two, three, and four. Fourth and final time. We got the Dallas Mavericks all the way down to the Hornets. All right, so here's how it shakes out. Matt with the Dallas Mavericks and the Houston Rockets. Will with the Warriors. Brian with the Bulls. Travis with the Raptors. Eric with the Sons. Robert with the Celtics and the Jazz. Peter with the Trailblazers. Robert with the Kings. Will with the Hawks. Matt with the Pistons. Steve with the Sixers. Matt with the Nuggets and the Grizz. Eric with the Nets. Will with the Timberwolves. Matt with my Lakers. Peter with the Clippers. And the Orlando Magic. Will with the Pacers. Travis with the OKC Thunder. Brian with the Spurs. Steve with the Bucks. Travis with the Cavs. Will with the Wizards. Brian with the Heat. Eric with the Knicks. Will with the Pelicans. And C Birch.  The Charlotte Hornets. Let's alphabetize by team name. Let's box this up right here. All right, and we're going to pause the video. When we come back, we're going to see if there's any trades. And then we'll have the break itself. Stick around. BRB. All right, welcome back, folks. No deals were done here in this one box break. So that list remains the same. This is the final printout. Hot off the presses. Thanks, everyone, for making this happen. I appreciate it. The next one box break is in the store. If you want to run this back, should be pretty easy to fill considering it's only a 10-spot break. There it is. The hobby edition right here. A lot of fun stuff. Good luck. Got the sounds of the Dodgers at Braves on in the background. Dodgers scored a couple runs in the top of the seventh. And the Braves came back scored a couple runs in the bottom of the eighth. And now here we are tied at four. In the top of the eighth, and the Dodgers down there last out. In the top of the ninth. Let's move on with this break right here. Good luck, everyone. Thanks. Nice LeBron James. And Wesley Matthews Red Wave. Not numbered. No vet commonship in this, but LeBron James does. So does Giannis. So does Luca. Second-year Jaumarance. And second-year Zion, of course. There's a second-year Zion. There's a Wesley Matthews Hyper. And a Hachimura Mojo. That's three. 23 out of 25. Nice. That's for Will and the Wizards.  Zion goes to Will as well. This almost looks like, the way the angle is, almost looks like D'Angelo Russo doesn't have an arm. Ooh, there's a Silver Giannis onto the Compo. And a James Weisman. Will with the Weisman. He also has the Warriors. And a nice Silver Giannis. Now, I don't, this is obviously not his rookie year, but Steve Birch with the Bucks. But people do love the Silver Parallels. Wonder what this could go for. He's a champion. Finally added that to his resume, which is nice. Hashtag good for the hobby. Silver Brandon Clark. Jason Tatum. Brooke Lopez. And we've got a Yellow and Black. That's out of five. Jaden McDaniels. Nice. I was about to say, I think these are really low numbered. This goes to Will Hatch and the T-Wolves. There you go, Will. Where there's a Will, there's a way. Which was his teammate, but still nice. Out of five. All aboard the Big Hit Express. Wide screen Luca. Obviously, that's an insert that would ship anyway. Even if it wasn't Luca, the inserts will ship. Zach Collins ships. That's a Silver. So will the Trey Young and the Jeff T. All right, next half. We haven't seen our autos yet. Oh, here's one coming up. Behind Troy Brown Jr. is Gordon Hayward Auto. Yes, Celtics autograph. Sensational signatures for Boston. That's going to be for Robert. There you go, Robert. Troy Brown Jr. going to Will Hatch. 110 out of 2.99. The red parallel. Troy Brown Jr. back there. Lou Will and Nancy Davis. And Purple Ice. Anthony Hardaway. That is 91 out of 175. Orlando. It's going to be for Peter and the Magic. And your second and final autograph is Rookie Auto. Tyler Bay. That's for Matt. Matt Lieber and the Dallas Mavericks. There you go, Matt. There's Isaiah Stewart, Hyper and Shaq. Shaquille O'Neal, 188 out of 199. And it'll be for Matt and the Lakers. Isaiah Stewart. Pistons have accumulated a lot of great young talent. So they could be a really interesting team the next year or two. I thought it was going to be his teammate for a second. Pascal Siakam Silver, Uduke, Azbuique, Red Wave for Utah. That's going to be for Robert. And a rookie Silver coming up. And that's going to be Cassius Stanley. Rookie Silver for the Pacers. That's going to be for Will. Nice Luka Donchich. Downtown Silver. Kawhi Leonard. Robert Woodard. Grant Riller. Also thought I was going to hit his teammate. Steven Adams. Daniel Tice, 210 out of 299. Nick Richards, Ogie Onoobi, and Zach Levine. There you go, ladies and gentlemen. A quick little one-box break of 2020-2021, Panini Prison Basketball. One spot gets you three teams in a one-box break. This is a hobby addition as well. So two autographs and a lot of nice parallels and still searching for some of the big names. I'm Joe for JaspiesCaseBrakes.com. I'll see you next time for the next one-box break. Bye-bye.


At Audiology Associates of Prestonsburg, you can live your life the way you want and find the freedom of better hearing. You'll experience patient care that is specific to you with exceptional follow-up care that ensures your hearing and balance needs are being met. Audiology Associates at 1428 Northlake Drive in Prestonsburg. With 2023 just getting started, many are ready to start the year off right with New Year's resolutions. However, many will fall short and abandon their New Year's goals within a few months. Mountaintop spoke with Michelle Martell to learn some tips on how to maintain your New Year's resolutions. Yeah, so New Year's is a time when a lot of people want to start fresh and make new goals, usually related to lifestyle changes. But a lot of times, I'll just speak from my own experience, people have trouble following through. And I think that's because a lot of white people don't know the tricks and the traits that behavioral psychologists know in terms of how to set good goals. The biggest problem people have when starting a New Year's resolution is setting a goal that is too high. Luckily, there's a trick for pacing yourself slowly to work towards your goal without putting too large a strain on your lifestyle. An easy acronym to remember is to set SMART goals and SMART, every letter in SMART stands for something. So S is for specific, M is for measurable, A is for attainable, R is for relevant, and T is for timely or time-sensitive. So a lot of people set pretty large goals at the beginning of the year, and that's where you hit that A for attainable. What you want to do is set something that is close to what you feel like you're already doing so that you can gradually make larger changes. We call that in behavioral psychology shaping. So starting with something small and then maybe using it to move more in the right direction instead of setting a really large goal. Many people are tempted to give up on their resolutions after faltering for one day. However, it is important to remember that progress is not linear and everyone deserves at least one cheat day. Staying determined and picking up where you left off the next day is the key to attaining your New Year's goals. For Mountain Top News, I'm Kelsey Dean.


Welcome to world's best videos. We've compiled the list of facts on social media sensation Lele Pons. Let's get into it Eleanor Pons or better known as Lele Pons was born on June 25th 1996 in Caracas, Venezuela She moved to US at age five. She lived in Miami, Florida Lele finished school from Miami Country Day High School in 2015 and moved from Miami to Los Angeles At school she was bullied by her classmate for an accent and her nose She got her first phone by the age of 15. She was later introduced to Vine by one of her friends She's a social media sensation known mostly for her start on a six second looping video sharing app Vine She was the first viner to surpass one billion loops before the app was shut down She ranked in the top five most followed and had over sixteen point seven billion loops That helped her remain as the most looped person on Vine The content she is most notable for is for her videos consisting of practical jokes on herself Her friends and her family facts you may not know She had a New York Times best-selling author for her book surviving high school The book was co-written with author Melissa Della Cruz Lele was featured in the first seven minutes of the second season of MTV Scream She won the Teen Choice Award in 2016 for Best Viner She was nominated for four other awards throughout her fame On September 13, 2016, she was accused by social media star Amanda Cerny that Lele had been accessing her accounts, deleting her posts from social media and setting her accounts private so she could acquire new followers On November 15, 2015, Lele took to Instagram to reveal her nose job and displayed her before and after pictures She explained that she got the nose job to make her feel happy and confident She said that it was something that she always wanted to do and she waited for the right time to do it She was one of the main roles in Marshmallow's summer music video as this skate date She acted in YouTube Red's original series Escape the Night and Play the Hustler Well that concludes the video guys, hopefully you guys did enjoy and if you did remember smack that like button Let me know in the comment section below what you'd like to see next and if you haven't already subscribed, please do subscribe to keep up with the world's best videos


Hello and welcome to the session. I am Arsha and I am going to help you with the following problem that says proof that 2 sin square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 is equal to 10. There is no million method solution and we will evaluate the value of left hand side and show that its value is equal to 10. The left hand side is 2 sin square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 which can further be written as 2 sin 3 pi upon 4 whole square plus 2 cos pi upon 4 whole square plus 2 times sin pi upon 3 whole square. This can further be written as 2 times of sin 3 pi upon 4 can be written as pi minus pi upon 4 whole square plus 2 times cos pi upon 4 whole square plus 2 times sin pi upon 3 whole square which is further equal to 2 sin pi upon 4 whole square since pi minus pi by 4 lies in the second quadrant and in the second quadrant sin function is positive plus 2 times of cos pi by 4 whole square plus 2 times say pi upon 3 whole square which is further equal to 2 times sin pi by 4 sin 45 degree which is 1 upon root 2 nvm whole square plus 2 times cos pi by 4 is again 1 upon root 2 whole square plus 2 times say pi upon 3 is 2 whole square which is further equal to 2 upon 2 plus 2 upon 2 plus 2 into 4 which is further equal to 1 plus 1 plus 8 which is further equal to 10 which is the right hand side of the given equation. So, we have left hand side is equal to right hand side and thus n square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 is equal to 10. So, this completes the solution hope you enjoyed it take care and have a good day.


Part 1, Super Mario World, The Lost World Super Mario. Ah. A good game. Everyone wants. Mario. This story began last month, August 5, 2009. I was on the way to my work when I saw an old man selling old GBA cartridges near our office. I ignored it and proceeded to. My work. I proceeded to my office, booted up the PC and chat with other office mates. I was surprised to see a kid in our office. I asked his name. He said he is Jerry. One of my office mates' child. He was busy playing his GBA at his father's desk. Suddenly, he went to me. Hello. It seems that you have a great time playing with Super Mario aren't you? Nope. I think this game has glitch. He asked me if I can fix his Super Mario World cartridge. He also said that the cartridge was a newly bought one. He and his father bought it from the store outside the office. He was excited to see it, but the game was too glitchy. I opened up the cartridge and I see that the saving system has been destroyed. I opened my cabinet and inserted the new one. I checked the board for more errors. So far, there are no further damages. I opened my GBA and inserted the cartridge. I insert a GBA ear loops to hear any glitch on the game. I was really creeped out to see. The title screen was filled with glitchy red mountain background. The music was in a low pitch tone. It's like the bass music when you are inside Bowser's castle. I pressed start button. Then I heard a really really loud and slow voice. It says, here we go, Super Mario. I pressed the A button continuously to skip. That horrible thing. The map showed up. I was really really creeped to see the ocean red. And some stones as violet. The ground is color brown and the path is color gray. The music is so slow. And also, the Yoshi's house is now Ice Hughes. Some names are also strange. Such as Gray Switch Palace, Yeez L&D1 and Booze House. I played the Ice Hughes. My eyeball nearly popped when I see dead Yoshi everywhere. Blood is dripping from the green tree, but the green tree is now gray. I immediately went of the screen and went to the Yeez L&D1. At first, no one's there. I run earned some one ups, mushrooms, and a cape. Feather. Near the end, there is a headless chasing chuck I tried to spin jump over it. Several times but it doesn't make any sense. I proceeded to the finish line. I was now in the Gray Switch Palace. The strange about this is, the stage has only one room.  I pressed it and everything seemed to be normal. But after pressing it, other levels on Yoshi's Island was now unlocked. I go. Inside the Booze House. The first and second room seemed to be normal. Same music is. Playing. The music was same from the title screen up to the stage. But after going inside. The boss door, I screamed. I saw red background with a real dead kid on the background. It. Looks like a picture inserted onto the stage. A big Boo was chasing me and I am on A. Moving platform where Iggy was. I spin jumped over the Boo. A loud voice said, Boo. Super Mario Dead. I turned the GBA off. My boss caught me. Playing and scolded me. After the ten minutes of decoy work, I removed the cartridge to. My GBA. I immediately connected the cartridge to my computer. Beside the ROM is a text. File. I opened it and saw this, thank you for playing Super Mario World, The Lost World. I opened the internet and searched for the binary text. It was, Evil Mario 666, I copied the ROM file to my USB drive and compiled it to. Another empty cartridge. I deleted the ROM and inserted a real Super Mario World game. I. Also changed the saving system, again. I gave the fixed cartridge to the kid. Jerry was. Really happy to see the new game. After the office work, I look at the GBA cartridge. Vendor. But he was now gone. At the exact place, I saw a cartridge with a 666 written on. Pental Pen. I hope I didn't pick it up. It caused a huge trouble. I go up the office and. Insert the cartridge in my cabinet. I went home safely. Part 2, The cartridge map After getting the new cartridge, the next day, I opened up my PC. I prepared the cartridge I got from the place where the Super Mario World, The Lost World vendor was. The cartridge has a torn sticker with a note saying the cartridge map. Written in faded Pental Pen. I was planning to insert the cartridge so I can access it on my computer. Suddenly, my boss called me. I left the computer and the cartridge unplugged. My boss scolded me for being so sleepy at work. Blah blah blah, etc. I didn't listen to. What he says. All that matters for now is about the cartridge vendor. After for almost 15 minutes of scolding, I went back to my desk. And I was surprised to see the cartridge. Inserted and my computer shut down. I immediately unplugged the cartridge and talked to my deskmate. Gary. Did you inserted this cartridge on my PC? What? Can you see what M? I doing? I am doing what you should do. Get back to your work man. I ask others if they inserted the cartridge. But no one said yes. I returned to my PC and booted up. My antivirus window appeared saying 1,566 threats has been successfully quarantined and removed. Virus has been removed upon reboot. I checked the virus names, sality virus, malware, etc. I run an immediate full system scan. No virus was in my PC. I downloaded a new firewall and update my antivirus and proceed to my work. The cartridge is still bothering me. After our lunch break, I returned to my desk and activate all firewalls and antivirus. I plugged in the cartridge and I'm surprised to see plenty of virus. It was like 5k+. I had a hard time plugging in and plugging out and plugging in again. Cartridge. But at last, after for almost 8 reboots, I successfully cleaned up the cartridge. The next day, I went and finished my work early. I plugged in the cleaned cartridge and I'm surprised to see thousands of virus. This time, I didn't make any reboot. I checked what's inside the cartridge and I saw a ROM file, text file and an un-executable robotics.rar file. I checked the text. It says that, copy the robotics.rar to the main ROM. It will jam connections and prevail hackers to see and edit the ROM. Please. Beware that after inserting the file, remove it quickly to prevent tormenting malware. Attack. As after reading this, I scanned the rar file and found that it is a pushbutt. I. Immediately delete that file and send to quarantine. I made a virus clean up then I reboot. My PC. After opening the ROM, I was surprised to see hundreds of games installed on the ROM. The ROM has mixed games of Mario, Pokemon, Sonic, Barbie, and so on. In the far end of the list, I saw a game named cartridge map. I opened that game. But actually, it's not a game. It's a map of the current city where I am now. It looks like a Google map. There are blue points and one, red point. One of the blue points is the location where the vendor was. It was like a motherboard. The path of electricity represents a road. Something like that. The red point is bit far from our office. The red point was almost 3 to 5 miles away from ours. I planned to get to that point. I prepared myself. I went to the office the next few days to resume my job. After two weeks, I packed up and I went to the red point. I forgot the cartridge map on my desk. But fortunately, I have written down a small map on the back of my journal. I went to that location. But as I go near the red point, I found something strange. I checked my phone and I saw that it has no signal. I checked my GPS and its battery is drained. I opened my palm top. But it doesn't making any response. All I can see with it is error connection 102. I continue walking. I made it to a small, abandoned looking building. I went inside and I'm surprised to see horrific pictures on the wall.  I was not comfortable to see it so I went outside and I was shocked to see the cartridge vendor was behind me. I ran as quickly as I can. I stopped on a 7-eleventh store. I went inside and bought some hot dogs. I seat on a vacant place near the window. While eating my food, I checked my phone and I receive a new message, there's a little signal now. I went to my inbox to check it. An unknown number. He says, I'm watching over you. I click the exit button and keep my phone. I went up and consume my food. I looked to the window and I'm surprised to see the cartridge vendor was now in the other road selling his old game cartridges. I ask the cashier if he knows the man selling old GBA cartridges. Here's what he says, do not ever talk to him and do not ever talk about it. He's evil. He continued serving the man on my back. Vendor turning around. It's the point that I noticed that the person behind me buying something on the cashier was the vendor of the game cartridges. I immediately turned again and talked to him. I said, who are you? Hey I'm talking to you. Bring back my cartridge. People on the shop all turned quiet and look at us. Three of them looks like scared. The vendor turned his back and go to his stand. I went back to my house. I have some nightmares about the pictures I see. The next day, I checked out the new on the headlines. The headline was written in bold black and thick letters, old cartridge vendor man. Missing. I went immediately to the 7-Eleven's and I ask the cashier about it. He doesn't reply. Whatever I ask. I went to my office. I know, boss would scold my because I'm late. But this time, it's different. Everyone was rushing and look like scared. Our boss talked to me, saying, help us remove this plague. I asked my seatmate Gary on what happened. He says, one of our office mates, Leo, tried to insert the cartridge. He played the cartridge. After long hours of playing, he went to the CR. The other officemate found him dead on an office cabinet. Blood were spilled over the cabinet door. Behind the dead Leo is a message written with blood, give it back. After that, virus attacked the system violently and delete huge amount of data. I checked my PC and I was so surprised to see the picture of the cartridge vendor dead with all cartridges surrounding around him. I stole the cartridge map and went to the red point. I threw the cartridge inside the building and went away. Immediately, I saw a text message on my phone, thank you, from the similar unknown number. The next day, I checked the newspaper. I saw the cartridge man dead with all cartridges spread all over around him. The cartridge map was staying on the top of his head. 12.45 noon, I got a new delivery. I was creeped out to see so many cartridges owned by the old cartridge vendor. I put them all to my warehouse, part 3, finishing my job I know, at this point, I was thinking that I really should not have done that. But in a long run, fixing that insane cartridge is a good work. And I don't really want to do anything bad. I want to make Jerry happy. But following the cartridge map, it's insane.  I think of what should I do with them? Suddenly, I got a new message from that unknown number. He says, help me. Well, the old cartridge man is dead. You know that. And why is this old cartridge man still sending me text messages? I searched my contacts to see anyone, or anything who can help me. I found a number of an old best friend. It's Rhodes. Rhodes is an IT technician. He finished studying with his massed-arrow degree of being an IT. He is more knowledgeable than me. I mean it. I called him. We talked about the cartridges and I tell him about the old cartridge vendor. He agreed to meet up with me tomorrow. I packed up the cartridge. I prepared my old GVASP. I woke up early in the morning, fixed myself and went to our meeting place with Rhodes. We went his house. We opened up a total of six computers, four PC and two laptops. He brought out three GVASP. I think I will not bring out mine. We inserted the connector to each computers. First, we enable all antivirus protection and firewall to all PC. Then, we cleaned up the cartridges. We tried to plate each cartridge. Some are really not working that looks like an unfinished glitchy game. We made a record of all the cartridge. The next day, we found out that all of the game cartridges are unfinished and something scary will appear at the end. We now, then tried to insert the cartridge on the connector. Each cartridge has the same number of viruses 1,566 each. And if you did unplug the cartridge, the 1,566 virus will still be there. So before unplugging the system, you should remove the robotics.rar. Implant it on the cartridge to successfully clean up the cartridge. We copied it. Robotics.rar files. After cleaning all the cartridge, we inspected the robotics.rar. With different programs. We found out 8 pushbots that recreates binary codes upon deletion. Nothing seems unusual. We replaced all fake horrible ROMs with a new working ROM. We also replaced the saving system and many other elements. After replacing, we are ready to go. Within 5 days of working, we made a stand at cells working cartridges. I was ready to pack up when I saw the cartridge map below my bag. I immediately turned on. My GBA to check if it has been cleared. Inside was a dialogue box. It says, thank you.  It's a big static noise. This caused me to be dizzy. The static noise was like a supersonic tone that really pierce your ears. The tone has a very loud frequency. After the static noise gone, I fainted. I woke up. I was surprised to see. I'm in my office desk. I turned around and I see Leo alive. I talked to him. Leo. You. Alive. Is this real? What are you talking about? Are you still dreaming? I'm 100% Alive. My boss scolded me for talking to Leo and not finishing my work. I checked the office cabinet and there's no blood stains. I asked the office mates about what happened. I asked Alice. Alice. What happens yesterday? Dude. Are you drunk? You're doing your work. Yesterday. You're so happy yesterday because it's August 4th and today is payday. You. Know that. I almost faint when I heard it. I checked my cell phone and I'm so surprised. To see the number of the cartridge vendor. His message says, thanks for finishing my job. Good work. A few hours later. I saw Jerry, playing the Super Mario cartridge that I edited. I take a little look while he is playing. All elements are now normal. Nothing's wrong. I asked Jerry, hello. It seems that you have a great time playing with. Super Mario aren't you? He replied back, yes sir. Thanks for fixing this. He smiled and continued playing the game.


Če. Če so, občasno zrbišam, nekaj pa nekaj nebo veseli. Imamo, da je to, kar je svek še, da je zelo izunili, in da je zap rebellijačne in zelo, da je ta propren, nekaj je to, da je zelo, da je to, da je to zelo, nekaj je, da je to zelo, da je to zelo, nekaj je to, da je to zelo, nekaj je to, da je to zelo, In najbolj teželj, da se počunja, da teželj vse, da je očaj naša, da teželj bo, da vse počunja, da je naša, da je očaj naša. Zdaj, izgledaj se za ovaj ljubi za taj možus. Iroč da vsi nas začelj, imam Behan z SAP. In sem vsečen na vsečenu OpenStack CPI projekte, in sem vsečen na vsečenu OpenStack projekte. Mi je Konega Šumaha, sem vsečen na Zuse Linux, sem vsečen vsečen na vsečenu Cloud and Systems Management Departement, tako da smo vsečenu OpenStack, in sem vsečen vsečen na vsečenu Cloud Foundry initiative, da smo vsečenu Zuse, da smo vsečenu in vsečenu in vsečenu. J敏lepeljno resipićo in zvoj očnega na plaque, da smo vsečenu zuse vsečenu OpenStack, tako da smo vsečenu počatno vsečenu. Skupajte vsečenu, da smo vsečenu in vsečenu vsečenu na Cloud Foundry. Zato sem jaz bore down ml Shah. Sudi sem zelo vsečenu, in zelo vsečenu posledajte vsečenu, kako jer izvradi, in so. Zelo, da je to veliko in občasno projekte. Tko je to poživno, da je tudi vse, da smo počučati, kaj smo počučati, da smo počučati. Zelo, njih ne. Zato smo počučati. Ne, da smo počučati in se počučati. Proste, da me ne bošte. Ne, da se ne bošte. Ne, da se ne bošte. Ne, da se ne bošte. Ne, da se ne bošte. tako da prej vse ne idete, ne bovre, ne bude koženje, ne bovre, ni ne bovre obč mixture, ne bovre, subtitelje, ne bovre, ne bovre, ne bovre, ne bovre, ne bovre, na navam, ne bovre, ne je robil konfigurati, ne bovre's, ne bovre, ne bovre, ne bovre, ne bovre, ne bovre, ne bovre, ne je tako zelo, ne bovre, ne bovre in ne bovre. Dobro ne je bil, kot čut ven vse. So, are you okay with Kilo, or Liberty, or maybe Mitaka? What do you need? Just tell me what you need, and I will set up an open stack for you. Hmm, it sounds complicated. I don't know. I'm just a developer. I want to deploy my crowd founder, and it just has to work. Sorry. Yeah, so, can you give me some instructions how to do that, and tell me away how to check that my installation is good for you? Yeah, yeah, you are lucky. I'm working on the Bosch OpenStack CPI project, and we have a test suite, which you can use to validate the OpenStack. You know, it's easy to set up the automated tests. You just have to set up concourse. It's a concourse pipeline. Concourse is a CI system, which supports pipelines. To do this, first you have to deploy a director. Then you can deploy concourse, and after that you can configure and upload the pipeline and just run it. So, basically, first you need to prepare an OpenStack project to deploy the director, just create a project, some networks, people, security groups, and so on. It should be easy stuff for you. I think it's... After that, you can go to Bosch.io. There is a sample manifest how to deploy the Bosch director. Just copy it. There are some properties which you can have to replace, and then Bosch deploy will work. And when you have the Bosch director, you can go to the beautiful web page of concourse, and then you can find instruction how to deploy concourse. It's just for the steps. It should be easy stuff. And after that, you can configure the pipeline. There are some properties which you have to set, but they are well-named and self-explaining. And, yeah, it should be easy. And then you can run the automated test pipeline. And, yeah, don't forget to execute the manual validation steps described on cloudfoundry.org. Does it answer your question? Can I get an answer until tomorrow? Oh, okay, yeah. Sounds straightforward. I didn't get the first thing at the second thing, but I will try my best and follow the instruction. It seems a little bit complex. So isn't there a better way how to do that? Maybe, yeah, maybe you have some feedback for us, and we can improve everything. Okay, so that's where we started. So this is how we got into that. And if you go to the next slide, we saw that there is actually a need to have all these instructions, all this expert knowledge, all these things you need to know to be able to answer the question. Is my OpenStack ready for cloudfoundry? Can I actually run Bosch on it? Can I run cloudfoundry on top of it? It's documented, but there's a lot to know. And there are many situations where you actually need to answer this question. So when you set up a fresh system, you need to figure out if it actually works. When you update your OpenStack installation, you might need to recheck if it still fulfills the requirements. Also when you have some trouble with running it and there's some issue that something breaks, it would be nice to be easily be able to check if it actually still works and if everything is in place you need so that you don't have to start with debugging your OpenStack instance before you actually get to your Bosch or cloudfoundry deployments. So what we thought is that it actually would be nice to put all this expert knowledge and all these instructions we have seen, briefly seen into something which is easy to use, which is as easy to use as the other tools you use when you are using cloudfoundry. Pushing applications is so easy. Just one command and everything works and you don't need to know about all the complexity behind that. So taking this period of simplicity, we thought it would be really nice to have one tool which encapsulates all these questions and gives an answer to this question, is my OpenStack ready for that? And that's where we started and where we started to develop something which gives an easier answer to the question, will it run on my OpenStack than all the manual instructions? Yep. Before we dive in deeper, let's take an overview what kind of scenario we are talking about. So we are talking about an infrastructure where you have OpenStack as infrastructure. We have cloudfoundry on top of OpenStack and maybe there are services which are running on top of OpenStack and cloudfoundry apps. These artifacts are building your product and we have Bosch, which is a release engineering tool. You can use Bosch to deploy your product to manage the lifecycle and monitor your product. And Bosch interacts with the infrastructure. To do this, Bosch uses CPI. In this particular case we have the Bosch OpenStack CPI. But there are also CPIs for all other infrastructures which Bosch supports, for example AWS, Azure, or vCloud vSphere. And Bosch is talking with the CPI over APIs, which are the same for all the infrastructures. And the CPI translates the API calls to infrastructure-specific calls. So on this picture we can see that there is Bosch, who has some requirements to OpenStack and we have your product which is also running on top of OpenStack and has its own requirements on OpenStack. So, what we have developed as a solution is a test suite called OpenStack Validator. It's implemented in Ruby and it's just test cases which are run by Aspect. Aspect is a test framework. So we have different kind of tests here. We have tests which are going through the CPI. So they call the same APIs which Bosch is calling using. And we have different tests which directly calls OpenStack APIs to tests like API rate limit or API versions and so on. And we have also tests which use SSH to SSH into VMs in the OpenStack environment. And, to test whether you have internet connectivity from the OpenStack to the outside or how is the connection between VMs in the OpenStack. Can you ping one VM from another? So, you can see that we want to validate OpenStack for Bosch but also for your product. And it will be possible also to implement, extend this validation test suite and implement your own test for your specific product. Let's have a quick demo. I am not going to run now the validation test suite but we have the current state of the validator has these test cases. It's just an executable which you can run. You have to provide CPI release which is used to run the test. Also a stem cell version stem cell, Bosch stem cell which is used to launch the VMs and also a configuration. The validator wants to know where your OpenStack is how to connect which project, which network, and so on. And optionally you can provide also a working directory. And the test, they say what's possible and what's not possible when something went wrong. There are error messages which for now doesn't look so good but we are planning to implement a custom reporter custom formator for our spec and you will get very nice error messages and also hints when possible what can be changed to improve this or to avoid this error. And a test case looks this is a typical test case with the CPI. It's you have a helper method where you can provide an error message. When something went wrong, the error message will be print out and also you have the CPI in the context and you can execute an action with the CPI and validate the error message at the end. The result. So to sum up the way to is unexecutable, you need a configuration, CPI release and stem cell it will extract everything, install the CPI use it to execute the test and at the end you will get a nice error nice report about what's good and what's wrong with your open stack. So, Cornelius, does this works better? This looks much easier. That's something I can remember. With a tool like this, I can work and I don't have to know about all the places you showed me before. This sounds great. Cool. I will now go a little bit into the experience we gained with that. As a little bit of background we started to work with SAP on the stack CPI, the cloud provider interface for open stack of Bosch end of last year and we started the collaboration and part of that as one of the first things we did was setting up a test system to actually run the CI for open stack on different versions. So we got started with setting up a system and one of the things which emerged there which we came back again we had to communicate what do we need to set up how do we need to configure it what are the right settings we had to communicate that within the groups which were involved with that, setting up the open stack instance, setting up the configuration providing the network and so on. And one of the topics which we came back to was that actually it's not so easy to define that and it's documented and you can try it out but there was a lot of experimentation involved so this topic and of course actually having a tool to check it would simplify things quite a bit and to go a little bit more into the specific experience here so when we set things up one thing we do a lot for open stack testing is actually setting up open stack in a virtualized environment with nested virtualization which works great for some use cases but in some cases the performance characteristics is not what you want because the nested virtualization actually takes some performance away so that's one of the things we ran into that we started to set up a nested virtualized open stack instance but then when actually deploying we realized it runs for a long time and it compiles things and the performance there actually is not sufficient and not what we would have expected so this was something which was we ran through just trying to set things up but then in the end we realized okay that's not good enough we have to do it in a different way also some other things for the network configuration that's something which is there are many options and it depends on how you set it up how you give access to the open stack system the questions of connecting within open stack from the open stack instances to giving access to the people at SAP to the test system so they could access everything with the same, with the right level of access also with HTTPS so this was also something which needed a lot of manual settings setting security groups setting up firewalls setting up the network there and some manual steps to just test does it work or not and some iterations to go through to just have one answer is my network setup correct do I have everything in place and have a simple green answer or a red answer with a note okay please add this port or add this service so that was another area where it would have been nice to have something there also another part of the network setup MTU settings are always something depending on how you set things up how you layer the networks in the right way also depending on what kind of technology use there, what kind of settings to use there and that's also something where we ran into some issues where we just thought can you please tell us how to do it what to do and what settings do you need and basically the answer was make it work just has to work and that's actually what we wanted to do but to get into the explicit details we had to put together the expert knowledge and figure that so from this perspective it would have been nice to actually already have this tool and bien just showed to be able to tell is my OpenStack instance ready and give an answer to the questions okay what do I have to do to to make it ready so from this perspective we started that's the state where we are right now and so for the future as a small outlook how we want to continue with that what would be possible to do there so at the moment we cover mostly the Bosch specific area we use the CPI there which is nice because it uses the same interface the same tool what actually then the production code would use but we want to cover the full stack so that we really have a conclusive answer as much as that is possible maybe the OpenStack layer but also covering the Bosch layer covering the Cloud Foundry layer and make this more complete and for this of course some things might be implicit or might already work you might run into issues when working on this when setting up new things or when changing things so there it has to be some kind of continuous improvement so we can actually run into so let's add an additional check to check that so that we can share some of this experience and make it more simple for more people so this is where we I think need some continuous improvement and some adding things and for that also it would be nice to make it more easy to at least test add some kind of plug-in interface or something so that you can also customize it for your own needs so maybe you have a product which needs specific features specific settings so that you could just easily add this to the test tool and then whoever is setting up your OpenStack instance to run your product on can just easily call the tool and get an answer for this product I need the specific setting or something so this is more or less OpenStack focused but as we showed we are using the actual CPI interface so we have some tests which are specific to OpenStack but most of the tests actually already use the abstraction layer which also Bosch uses to abstract the cloud specifics so with this in mind it actually would be quite easy to extend that to other platforms and to other infrastructure as a service systems so that we could share most of the test code to actually do the testing through the CPI and we wouldn't have to write specific the full stack of tests again and again for every other cloud infrastructure you might want to use below that so this isn't topic which we are interested in also to get some discussion get your input what you think what would work for you how we could extend that what would be useful and how we can put that together with other things which are happening and that's where we are going the code is open source so if you want to use that it's on github in the cloud found reincubator project so you have the URL there you will find it there and we are here open to discussions we also have a package for those of you who use the suzer operating system we have an RPM build in the build service where you can actually just download the validator and you can just execute that and we are open to discussions so please talk to us give us your comments and tell us what you think thank you so are there questions right now combination or a set of combinations that will work in this version of stencil etc are there tests in that to recommend that and the second thing which I have noticed on watch.io initially in the past there used to be documentation for example if you are thinking of this stencil this is the combination of cpi where you have stencils what will work probably you lost it maybe I am not able to see it that range is being maintained the question is one part of the issue is to validate open stack and the other one is which combination of cpi stem cell should I take this for the open stack we are working on this in the future there will be on watch.io you will have a range of stem cell and cpi which are tested together and yeah it's an ongoing effort it will be there are there other questions no they are implemented in ruby we don't use now tempest we are in discussion about this and maybe we can combine efforts in the future but for now they are implemented in ruby yeah at the moment we are coming from the Bosch site so using ruby as a language using the cpi to interface with open stack tempest is on the other side so there certainly is some combination possible at the moment we are coming from the Bosch site ok, thank you and bye


So in last lecture we were discussing the notion of subspaces, okay. The topic for today is linear independence of vectors but before that there are certain aspects of subspaces that are important which I would like to cover, okay. For instance how to get new subspaces from old? Let us first address this problem. I have a vector space with two subspaces, okay. Then I get a new subspace by looking at the sum of these two subspaces. I will define W as W1 plus W2, sum of sets, sum of two sets. What is the definition? The definition is it is a set of all x plus y such that x belongs to W1 and y belongs to W2, okay. I am defining the sum of two subspaces W1 and W2. The notation is W1 plus W2 I am calling that as W. This is a collection of all x plus y where x comes from W1, y comes from W2. Now collection of all x plus y or y plus x does not matter because addition is commutative, okay but let us stick to this notation. The first one will come from W1, second comes from W2. Then this is a subspace. This is a subspace of V. Why is it a subspace? It is easy. Just appeal to the theorem that we proved last time. We need to take two elements in W, show that their sum is in W. Take a vector in W, take a scalar multiplication. It is close with respect to that operation also. So once you show that then it follows this is a subspace. So I am going to leave this as an exercise. W is a subspace of V. This is an exercise for you, okay. Now this is in some sense larger than W1 and W2. Let us look at something that is smaller than W1 and W2. So that is another subspace. Let us call it Z as W1 intersection W2, the Z intersection, okay. Then I am going to leave this as an exercise for you to show that this is also a subspace. Z is a subspace of V. This has a property that this is contained in W1 as well as W2. So you can think of this as a subspace of W1 as well as W2, okay. There is another method of getting subspaces. Let me describe that. Let us take S as a subset of V. I will define the span of V, the span of S denoted by Sp of S. I am going to define this as the set of all linear combinations of elements of S. I have not defined what a linear combination is but I will do this now. The span of S is the set of all linear combinations of elements of S. So mathematically what is span of S? Span of S is the set of all alpha 1 V1 plus alpha 2 V2, etc, alpha K VK where the alphas are scalars, VKs are vectors in S, okay. So alpha 1, alpha 2, etc, alpha K they come from the field and V1, V2, etc, VK they come from S. Now this is what I am calling as a linear combination. This will be specifically linear combination. This is a linear combination of the vectors V1, V2, etc VK. This is my definition. A linear combination of the vectors V1, V2, etc VK will be called a linear is a typical element of spanners and it is of this type. Linear combinations of this form that is a typical element of span of S. Now this span of S is a subspace, okay. This span is a subspace of V. To prove that this subspace of V again we will use that theorem close with respect to addition and scalar multiplication. The proof is there once you write down the first step correctly. This is a subspace of V, span of S is a subspace of V. The proof you are going to tell me the first line and I will just leave it at that. We want to show that this is close with respect to addition for instance. Scalar multiplication is similar close with respect to addition. So I need to take two elements. Let us say U comma W belong to span of S. We must show that U plus W belongs to span of S, okay. I wanted to just tell me the first line after this. How do you prove that this belongs to span of S? Okay. Quite a few seem to know the proof.  U is in span of S so it is a linear combination. So I have something like this.  See it is just some linear combination. Please remember that it is not the same k that we have here. Finitely many terms V sorry W I will write a similar expression for W delta 1 W 1 plus delta 2 W 2 etc plus delta R W R. In general this R and L are different, okay. Again now for some delta 1 delta 2 etc delta R from the reals and W 1 W 2 etc W R from S. This is the first step. This is the important step. The rest of the proof is obvious. U plus W now is a linear combination.  So it is close with respect to addition. Scala multiplication is simpler than this, okay. So span S is a subspace. Let us look at one or two examples of span of a certain set. See remember this S could be an infinite subset. This S could be an infinite subset, okay. But for illustration let me take the following two examples. First one, let us take S to be V 1 X 1 X 2 where X 1 is a vector 1 0 1. X 2 is the vector 1 1 0. X 1 X 2 are vectors in R 3, elements from R 3. S is X 1 X 2. The question is what is span of S? What is span of S? Let us try to determine span of S. Now you will see that what we have learnt earlier with regard to linear equation that will be that will come handy, okay. What is span of S is what we want to see? What we know is that span of S will contain linear combinations of X 1 and X 2. But what we want is a formula. A formula for elements in span of S, okay. Given a vector I should be in a position to determine whether this vector belongs to span of S or not, okay. Given a vector is there a condition that I can impose on this vector in order for this vector to be in span of S? If this condition is satisfied it is in span of S, if the condition is not satisfied it is not in span of S, okay. Let us try to derive one condition. You will see that this elementary row operations will be useful, okay. So let we are trying to determine this question. Let B belong to span of S, okay. Then what is B? That is the question, okay. What is B? That is how does B look like? That is the question. Now B is in span of S, okay. So let us write down the definition. B is something like alpha 1 X 1 plus alpha 2 X 2 for alpha 1 alpha 2 in R, okay. If B is in span of S then by definition B is a linear combination of these two vectors. Let us write it in full. Now this B is a general B in R3 we do not know how it looks like. So let me rewrite it like this. I will write alpha 1 X 1 plus alpha 2 X 2 on the left and B on the right. Then familiar linear equations could be used. Alpha 1 X 1 plus alpha 2 X 2, alpha 1 into X 1 is 101 plus alpha 2 into X 2, 110. On the right hand side I have the vector B. So it has three components B 1, B 2, B 3, okay. Alpha 1, alpha 2 are arbitrary. What must be the conditions on these three numbers B 1, B 2, B 3 in order for B to be in span of S? In order for this equation to be satisfied but this equation you will see is precisely the following linear equation. One homogeneous linear equation. I can write it as follows, okay. Can you see it is precisely this? Okay just tell me if this is okay. That is we seek B such that A alpha equals B where A is the matrix whose columns are these two, 101, 110. Alpha is the vector of unknowns alpha 1, alpha 2 and B is of course B 1, B 2, B 3. We are seeking to solve A alpha equals B. Do you agree with this? Just write down the three equations. First equation alpha 1 plus alpha 2 equals B 1, alpha 2 equals B 2, alpha 1 equals B 1. Those are the three equations in two unknowns alpha 1, alpha 2, okay. Let us do elementary row operations. That is I want to now determine all B for which this system has a solution. I know how to do it by using elementary row operations. So I need to look at A appended with B, 101, 110, B 1, B 2, B 3, okay. I do the elementary row operation reduces this to the row reduced echelon form. The final step tells me what must be B, okay. So this is now row equivalent to I will keep the first one as it is, 101, B 1. This will also be kept as it is minus this plus this 0 minus 1, B 3 minus B 1, okay. Next step one more operation. I can actually stop here but I will reduce it to the row reduced echelon form. So let me just do one more operation for the sake of completeness. Second row is 0, 1, B 2, okay. Now it is in the row reduced echelon form. The number of non-zero rows of this is R for me. This whole thing is R prime. This is R for me. This is D. I have R alpha equals D. I have R alpha equals D, right. This is R. The number of non-zero rows is 2. The necessary sufficient condition for the original system to have a solution is that this must be 0. So A alpha equals B has a solution if and only if B 1 is B 2 plus B 3. Now that is the condition for any vector to be in span of S.  So this determines the subspace completely, okay. Let us modify this example and just do one more. You will see how the notion of homogeneous equations, non-homogeneous equations, invertibility, etc that we had studied earlier will be useful once again. So I want to look at another example, modification of this. This time S will be for me X 1, X 2, X 3. X 1, X 2 as before, okay. X 1, X 2, X 4 as before. X 3 is this vector 0 1 1. I would like to determine what is span as now, okay. What is the span of this set? Now again we will have to look at something like this, okay. We seek B such that A alpha equals B. This time A is a 3 by 3 matrix, 0 1 1, alpha is alpha 1 alpha 2, B is B 1, B 2, B 3, okay. So I will have to do the elementary row operations. Let me remove this as before. To determine the span S completely we need to solve the system A alpha equals B, okay. This time A is the matrix whose columns are the 3 vectors that we started with, okay. So we need to append this 0 1 1 and then B 1, B 2, B 3, okay. Let us do this quickly. This is row equivalent to, first one I am going to keep it as it is, right. B 1, okay. Next step, this is row equivalent to, okay. Let us see what we could do, okay. Then I will divide this by 1 and then rewrite this like this and then keep this as the pivot row, the operation performed with respect to this row. This whole thing comes here, okay. Here I have to just add 1, 0, 0. I have another expression here. Please fill up. This will be the sum of these two terms, okay. But whatever it is, now observe that this is R for me, R alpha equals D. This is R. Then I am reducing the system A alpha equals B to R alpha equals D. The number of non-zero rows of R is 3 and so which is precisely the number of rows of R and so there is no condition. This D i is equal to 0 for i greater than R. That condition is vacuously satisfied. So this system has a solution for all B which means what? So A alpha equals B has a solution for all right hand side vectors B. So what is span of S? It is a whole R 3, okay. It is an improper subspace of R 3. Span of S is the whole of R 3, okay. If S is chosen as this set then span of S is R 3, okay. We will come back to this example. This will be useful when we discuss the notion of linear independence. So we are still discussing subspaces. In this example alpha is alpha 1, alpha 2, alpha 3. Yes, in this example it is alpha 1. Here I have to make a correction, yes. In this example there are, yeah that is correct. In the second example alpha has 3 coordinates, okay. We are still discussing the notion of subspace. There is one small extension of this idea of span of a subset which is what the so-called row space, column space of a matrix. So let me describe this and then go to the next topic.  The row space of A is defined to be as the subspace of all linear combinations of the rows of A. The row space of A is the subspace of all linear combinations of the rows of A. So what one does is to if A is an m cross n matrix there are m rows each row is an R n, each row has n coordinates. So the row space, so what one does is look at span of the rows, okay span of the rows that is set of all linear combinations of the rows of A. That is the row space of A. Let us observe that the row space of A is a subspace because just now we have proved that the span is a subspace. This is a subspace of R n. Each row has n coordinates, each row has n coordinates. So this is a subspace of R n. One can define the column space similarly. The set of all linear combinations of the columns of A, the column space is a subspace of R m. So let me just say similarly column space of A is defined and what I want to say is that the column space of A is a subspace of R m, is a subspace of R m, okay. So these two are subspaces of different vector spaces but they have a number that is the same. There is a unique number associated with these two subspaces. That number is the same for these two, okay. We will see that in a little while. Even though these are subspaces of different vector spaces, we will see that there is an important number that one would like to associate with a vector space or vector subspace for that matter. That number would be the same for these two, okay, okay. With this I would like to move to the notion of linear independence of vectors, linear independence of vectors, okay. Once we have this notion, we could define a basis for a vector space and then the dimension of a vector space, okay. So what is linear independence? Let us first look at linear dependence. Linear dependence among vectors. Let us take a collection. Consider a set of vectors. Let us say v1, v2, etc vk from a vector space v. We would like to say that these vectors are linearly dependent if at least one of them depends on the others, okay, informally. At least one of them depends on the others. One of them depending on the other. At least one of them depending on the other means you can write one of them as a linear combination of the others, okay. In other words, let us formulate this. v1, v2, etc vk are said to be linearly dependent. I have this equation to be satisfied.  If this is the zero vector, so I am defining linear dependence, okay, linearly dependent. If this holds without all of them being zero, yes, I will write it like this. This holds with not all alpha i's being zero. That is there is at least one alpha i such that this equation holds, okay. Now you will see that if there is at least one alpha i which is not zero, let us say alpha s is not equal to 0 for some s, at least one scalar is non-zero, then one could write down. See all that I want to demonstrate next quickly is that there is some dependence. That is at least one of the vectors here can be written as a linear combination of others. That is why it is called linear dependence. If this holds, then I have linear dependence, okay. Then observe that alpha s is not zero.  I have simply pushed the other vectors to the right hand side. Since alpha s is not zero, I will divide this by alpha s.  You fill up the details. I have written v s after dividing by alpha s. I have written v s as a linear combination of v1, v2, etc vk. On the right side I will not have the vector v s. This is linear dependence, okay. So this is a definition that conforms to what we fail intuitively about linear dependence, okay. What is linear independence? Linear independence is a negative of linear dependence. v1, v2, etc vk are said to be linearly independent if they are not linearly dependent, okay. Of course what does it mean in terms of that equation alpha 1 v1 plus etc alpha k vk equal to zero. We have the following.  This holds where I do not have linear dependence. So each scalar must be zero, okay.  That is linear independence there because even if one of them were non-zero, one could push the other vectors to the right, divide by that scalar to get this non-zero, to get the vector on the left as a linear combination of the others. So none of them should be zero. That is linear independence. One also says that the only way to get the zero vector by means of these vectors v1, etc vk is by the trivial linear combination. Then we say that the vectors v1, v2, etc vk are linearly independent, okay. Let us look at some examples. Let us look at some examples to consolidate. Take the example of the previous one, the span thing. Let me stick to the same notation. X1 is 101, X2 is 110, X3 is 011, okay. I would like to verify if these vectors are linearly independent. I would like to verify if these vectors are linearly independent. So I must start with a linear combination, okay like that. So consider a linear combination alpha 1 X1 plus alpha 2 X2 plus alpha 3 X3 equal to zero, the three dimensional zero vector, the vector with three components each being zero. Then again, okay let me write in this example to make it more transparent.  These are the three equations. Of course Gaussian elimination can be applied and then you can get the solution immediately but I will pretend as though I cannot do that. I want to use elementary row operations once again, okay. But let us recall what happened for this particular example. This is the same as, I will again use the same A that I used in the previous example. I am looking at the system A alpha equal to 0. I am looking at the system A alpha equal to 0. I want to know whether this system has a non-zero solution. I want to know whether the system has a non-trivial non-zero solution. What is A? A is the coefficient matrix here. Just write down these three vectors as columns. You get A. What is alpha this time? There are three unknowns, okay. I want to know if the system has a non-trivial solution but look at what we did earlier. For this matrix A, we had shown that the right hand side, look at the non-homogeneous system A alpha equal to B. We had shown that the right hand side needs no condition. Whatever be B, whatever be the right hand side, the system A alpha equal to B has a solution. Remember the result that we proved with regard to linear equations. A is invertible if and only if the homogeneous system A x equal to 0 has 0 as the only solution, if and only if A x equal to B has a solution for all right hand side vectors B, okay. So from what we have done earlier, A x equal to B has a solution for all B means that A alpha equal to 0 has 0 as the only solution which means if this system has a solution then 0 is the only solution which means alpha 1 equals alpha 2 equals alpha 3 equals 0 that is linear independence. So A alpha equals 0 implies alpha equals 0, the computations have been performed earlier. I am making use of that that is A alpha equals 0 implies alpha 1 equals alpha 2 equals alpha 3 equal to 0. So the vectors x 1, x 2, x 3 that we started with they are linearly independent, okay. Now what is the guess about the other example? The example where we had only the first 2 vectors x 1, x 2 just guess, do not look at the numbers, do not look at the coordinates. That is what is given is that you have 3 vectors x 1, x 2, x 3 you have shown these 3 are linearly independent. The previous example is x 1, x 2 my question is they are linearly independent, okay. The reason is something that we can prove in general any subset of a linearly independent set is linearly independent, okay. So like a precursor you can show that vectors x 1, x 2 from just if you take in fact you take any 2 of the vectors from this set they will be linearly independent that follows from a more general principle, okay. What about a different vector space instead of R 3? So I am going to look at example 2 really. Let us look at pk, pk is a vector space of all polynomials of degree less than or equal to k with real coefficients, okay. Let me pick these vectors. So I pick k plus 1 polynomials p i of t equals t to the i that is p not is a constant polynomial 1, p 1 is a polynomial which satisfies p 1, p equals t for all t, p 2 t is t square etc, pk of t is t power k. Let me conclude by showing that these vectors that is these polynomials are linearly independent. These polynomials are linearly independent. Let me take the case k equals 3 just for simplicity and consider a linear combination alpha, I will start with alpha not, alpha not p not plus alpha 1 p 1 alpha 2 p 2 plus alpha 3 p 3. I start with this linear combination I must see if I can show that all the coefficients are 0 then I could conclude that these vectors that is these polynomials are linearly independent, okay. Now this means what? This means see the set of polynomials is a vector space so this is also a polynomial. This polynomial takes the value 0, this is identically the 0 polynomial means at every t this is 0 that is alpha not p not of t plus alpha 1 p 1 of t plus alpha 2 p 2 of t alpha 3 p 3 of t. This is 0, this number is 0 for all t in R that is the meaning that is the previous one is identically 0 I should write which means you evaluate this at any t then the value is 0. Now you write it in full and see what you get, you get alpha not plus alpha 1 t alpha 2 t square plus alpha 3 t cube equal to 0. This is true for all t, how to conclude from this that each of the scalars is 0 that is the claim I am making yes one could use heavy machinery fundamental theorem of algebra a polynomial of degree k has precisely k roots, okay but we can we can do without the fundamental theorem of algebra that is what I wanted to illustrate in this example. See each is a polynomial, polynomial we know are differentiable functions differentiate this equation as many times as you want and get the desired conclusion. Differentiate once you get alpha 1 plus 2 alpha 2 t plus 3 alpha 3 t square once more 2 alpha 2 plus 6 alpha 3 t one last time 6 alpha 3, okay.  So this is a proof which does not use a fundamental theorem of algebra just use differentiability of these polynomials okay let me stop here for today.


What's happening guys? It's Shane here and today we're going to be talking about how much college costs, right? So there's a lot of information out there that you read on the internet on how much college costs and it varies greatly. So in this video, I'm basically just going to go over what it actually costs in my experience. This is after doing tons of research on it and also working personally with people because a problem with a lot of the data that's reported in these studies is just 20 years ago, college didn't cost nearly as much as it does now. And it also doesn't take into a lot of factors like how much your student loans are going to compound over the lifetime while you're paying them off. So the true cost of college is going to be different than a lot of the numbers that you hear. Before we get into that, make sure to gently tap the like button. We'll set a goal for this one of 1000 likes. And if you haven't done it already, of course, hit that subscribe button and ring the notification bell. All right. So how much is college going to cost when you include all of the expenses like renting a dorm room, all the supplies you have to buy as well as the tuition, etc. It is going to cost about 80 to $100,000 to get a bachelor degree. So that's over a four year period. It's going to cost 80 to $100,000. And the average student who takes out student loans is going to take out nearly $40,000, right? So you're going to go about $40,000 in debt and it's going to cost you in total if you include rent and everything about 80 to 100,000. Now there are ridiculously expensive colleges out there where you can rack up about $80,000 in one year. So for instance, Harvey Mudd College costs around $77,500. University of Chicago is not far behind and then Columbia is very expensive as well. But those are extreme outlier examples. But if you break it down even further, let's look at public, private, in-state and out-of-state schools. So a private four year school on average is going to cost $32,000 a year in tuition and fees. So that's about 128,000 for the full four years just in tuition and fees. A public four year out-of-state school, so you're attending a public school, but it's out-of-state. So therefore it's more expensive is going to be about 23,000 a year. And over four years, that's about 94,000. A public four year college that's in-state is around 9,400 a year. Over four years, that's going to be around 36,000. And a public two year college is going to be around 3,400 a year. And of course, you would only attend that for two years. That would be like a community college setting. So that's around six to 7,000 for those two years. Of course, I rounded down on all of these a little bit. So it's a little bit off, maybe by a thousand dollars or so, just to make it simple. So if you went to a private four year university for all four years, it would be ridiculously expensive. You'd be nearly $130,000 in debt. But if you did something a little more affordable, let's say you go to a community college for the first two years, around $3,500 a year, you'd be 7,000 in the whole. And then 9,400 for the next two years at an in-state school, that'd be about 18,000. So you'd spend around 25 to 27,000 for your total costs and fees of tuition to go to these two universities. First the community college and then the university. Right? So that's a lot more reasonable. That's literally saving $100,000 in tuition and fees just by doing that alone. But that's just the first part of the story because we're only talking about the debt that you accumulate while you are attending the university. Right? So you graduate with about $40,000 in student loan debt and then you have to pay interest on that debt. So what are the interest rates for undergraduate loans? They're usually around 3 to 5%. Currently or at least in the last year, they were 4.53%. And this is for the typical student loans that you would take out if you signed up for FAFSA. If you go to graduate school, student loans have an even higher interest rate. They're more like 7 to 7.5% if you take out grad plus loans. In 2019, 2020, nearly half of the students who went to college had to go into debt and the average debt was around $37,500, nearly $40,000. And collectively, they now owe $1.8 trillion. This is more debt than credit card loans. This is more debt than car loans. The only type of debt that beats this is going to be mortgage. So housing loans. Now you might be asking yourself, how long does the average person take to pay off these loans? And the answer to that is about 20 years. The average person takes around 20 years to pay off their college debt. However, the amount of debt that people have has gone up about 500% or five times since 1999, which is about 20 years ago. So people have been taking around 20 years to pay off their student loans, which were five times less 20 years ago. So who knows how long it's going to take them to pay them off into the future. It might be 25 years, 30 years, 35 years, maybe 40 years before people on average are paying off their student loan debt. And this is why it's so important with this current system, the way that it works, that you make sure to choose a degree that is going to give you a return on investment.  You need to make sure that it's going to pay off because people who graduate with good degrees aren't going to take all that long to pay them off. It usually takes them maybe five years instead of 20. And if you want to know in great detail how to choose your college degree, how to get the most out of college with the least amount of time, effort and money, check out my college 101 course down in the description below. That will absolutely solve your issues. But with that being said, I also go over this stuff in great detail on my channel. So check out my other videos right here. I made them just for you. Go ahead, hit that subscribe button, hit the like button, hit the notification bell and comment down below any thoughts, comments, etc. that you have on the video. And I will see you next time.


The Black Jewel Miner protest has not only affected the community of Harlan County, but also surrounding areas in Kentucky. Governor Matt Bevan spoke about this situation on Tuesday and what is being done to help the Black Jewel Miners. Yeah, I mean, it's a tragedy. When people get the rug yanked out from under them, as happened to our Black Jewel Miners down in Harlan County, and some who came in from surrounding counties to work there, it devastated this whole region, southeastern region of Kentucky in many respects. And so to that end, when you see people who not only are misled about the financial solvency, but then are asked to do work and then not paid for work they actually did, the company knew it was in trouble before they did that. It was very inappropriate. They have been fined. They will be ultimately reimbursing people as part of this whole bankruptcy. But in the meantime, it leaves a whole lot of people in the lurch, and kids going back to schools, and families trying to make medical payments and keep the light bill paid and food in the whole nine yards. The dignity in the class with which they have conducted themselves is awesome. It's impressive. And I'll tell you what, it reflects well on them, on the community, on Kentucky. They were done wrong, and they said we're not going to stand for it, but we're not going to do it in a way that hurts other people. And even when they let that engine go so that that engine would not disrupt another community's ability to feed themselves. What a powerful, high class statement that was. It made me so proud of them. That moment, I was already planning to try to get down there. But when I saw that, I said I'm going to go down and just thank them from the bottom of my heart, just for representing Kentucky so well. I would just simply say this help is coming. There have been community members that have stepped up to come around alongside folks. The Gilliams have stepped up with this foundation to provide almost half a million dollars in support. There is everything that can be done at the federal level is being done. There is a bankruptcy proceeding that has to follow procedure. There's a stocking horse. There will be sale of some of those assets. Those dollars will be used to pay back the liabilities, including for back pay that is owed to people. But I will say this, everything that can be done at the federal level, at the state level, and at the local level is being done.