The main idea for this section is the idea of a non-singular matrix. Those matrices which have matrix inverses, matrix reciprocals, you could call them. And therefore, division is essentially possible for non-singular matrices. Now, showing that a matrix is non-singular just comes down to providing an inverse matrix. It's like, oh, here it is. Everyone can see the inverse matrix. That's all the same thing you'd have to do to prove there's a big foot, right? All you have to do is just go capture him, right? And show him to the world, here's big foot. But what happens if there's no big foot? How do we prove that he doesn't exist? Because our inability to find him does not mean he doesn't exist. It could be that big foot's really good at hiding from noisy humans in the California forest or something, right? So non-existence, proving something doesn't exist is a much more challenging task. And so in this regard, we're gonna introduce the non-singular matrix theorem, which is a huge, huge, huge theorem for which we are not gonna even provide most of the details here. But what this is gonna do is it provides a list of equivalent conditions for a matrix being non-singular. And I'm not kidding on this. Like, I mean, if we look at this, if we look at this on the screen, I mean, this thing fills the entire page. We go down to xx, which, in Roman rule, that's 20, right? So this is a very long list of things. And again, some of these things are very naturally connected to each other, but let's talk about a few of the highlights of this list right here. So first thing, condition one, being non-singular means you're non-singular. That's sort of a no-brainer, because, well, if you're non-singular, you're non-singular. That doesn't give us any new information in this situation. Well, equivalent means that, when we say that two things are logically equivalent, we mean either both statements are true or both statements are false. And so when we look at this list of 20 items, which I'll warn you, this list is not comprehensive. These are just some of the items that are equivalent to being a non-singular matrix. When you have one of these statements as true, then it turns out all 20 are true. And if one statement is false, then all 20 are gonna be false as well. So if a matrix is non-singular, what does that mean? Well, first of all, it means that the matrix is invertible. That is, it has a matrix inverse, what we'll call that A inverse there. Now this A, one and two are obviously the same thing because this is actually how we defined non-singular matrices. So of course, a non-singular matrix, a matrix is non-singular if and only if it's invertible. But when you look at condition number three right here, this one might seem like it's the same thing, but it's a little bit different. We say that a matrix can be non-singular if and only if there exists a matrix C such that C A equals the identity. And so this right here would say that there exists some type of left inverse. Because after a matrix multiplication is not commutative, multiplying on the left is not the same thing as multiplying on the right. And so if there's a matrix which multiplies on the left of A that produces the identity, we claim that this is equivalent to having an inverse. That is, it's equivalent to be non-singular. So checking for a left inverse is actually sufficient to showing that a matrix has an inverse, all right? And then condition four talks about right inverses. There exists a matrix, which would multiply on A by the right, gives you the identity. So if you have a one-sided inverse, that's actually equivalent to having a two-sided inverse, aka a regular inverse. And so when we check, oh, are these two matrices inverses of each other? You only have to check one side. You don't have to do both multiplications because it'll always turn out to be the case with a square matrix. All of these conditions are equivalent to being a non-singular matrix. Condition five here says that if we look at the equation A equals zero, this is our homogeneous system of linear equations here. If this has only the trivial solution, because these things are always consistent, you can always take X to be the appropriate zero vector. We always have trivial solutions. But if there is no other solution, if the only solution to AX equals zero is the trivial solution for a square matrix, it's important in this whole conversation, we realize the matrix is square. If you relax that to an M by N matrix, many of these things will no longer be true because after all, only square matrices can have inverses. A rectangular matrix could not. If AX equals zero has only the trivial solution, that's equivalent to being a non-singular matrix. The matrix inverse will exist. And we'll actually see in the next lecture why that is the case. And that connects us to a lot of things, right? Because if AX equals zero has only the trivial solution, that means the equation AX equals zero has no free variables. And the existence of free variables has nothing to do with the vector on the right-hand side. AX equals B would have no free variables. That's exactly condition six right here. So there's some things we could say about that. Another thing to consider is that if AX equals B has no free variables, that means inside of the matrix, since we're a square matrix, you're not gonna have any rows of zeros when you row reduce A, which would mean that it necessarily is gonna be consistent because the only thing that can make the system inconsistent would be zero equal to something non-zero. So AX equals B is gonna be consistent for all vectors B, all right? Some other conditions related to that is that the column vectors of A are gonna have to be linearly independent. And if the column vectors are linearly independent, then they actually form a basis for the column space. And because of the independence, the dimension of the column space was at its rank, if you have a pivot in each column because the columns are linearly independent, that means the rank is gonna have to be in. And if the rank is in, that means the column space, which is spanned by the columns of A, would have to span the entire indimensional space, which is FN. So the columns of A span FN, they're a basis for FN. We can also make a statement that if A is singular, then its transposal also be singular because if you have a column, if you have a pivot in each and every column, where did it go, here we go, if you have a pivot in every single column, when you take the transpose, columns become rows, and since you have the same number of rows as columns, you have a pivot in every row, but you also have a pivot in every column still. So A transpose will be invertible matrices, which means that the rows of A will span FN because its column space would span FN. The rows of A have to be linearly independent. The rows of A form a basis for FN. So you see all these connections. Once we've kind of connected things together, we get all these other properties, right? And so I would encourage you to kind of read through this list of familiarize yourself with all these things equivalent to being a non-singular matrix. We've talked about free variables. We've talked about spanning and linear independence. We've talked about A transpose. Another one that's very important to mention here. So like, okay, A would have in pivot positions. That's the same thing as saying the rank is in. This one's an important one too. And this is actually our inversion algorithm, which we're gonna present in the next lecture. It's gonna be based a lot on this fact right here. A is row equivalent to the identity matrix. That is the same thing as being a non-singular matrix because if you have a matrix which has a pivot in every single column and it's a square matrix, that thing would row reduce to the identity. I want you to convince yourself of that. We can make a connection to matrix transformations. The linear transformation that sends X to AX would have to be an injective map if A was non-singular. That would have to be onto. It'd have to be one-to-one and onto, right? If you get one of the conditions, you actually automatically get both of the conditions, which is pretty impressive. And so this is just 20 of properties. This is not an exhaustive list by any means. Now some consequences of the non-singular matrix theorem I wanna talk about right now. A corollary that's actually quite interesting is that if you have a product of two matrices that's non-singular, then the two factors had to be non-singular themselves. This is sort of a weaker version of the zero product property. So with numbers, if you have X times Y equals zero, you would then say, oh, the scalars, that implies that X equals zero or Y equals zero. We couldn't do that for matrices. And that's because if you have a product of two things that's equals zero, it could be that the matrix that you have, you can have the product of singular matrices that gives you zero, even though they're non-zero themselves. So we don't get the zero product property, but we can get something kind of like unto it. If you have a product of two matrices that's invertible, that means that it's non-singular, then the two factors had to be invertible as well. And this is a consequence of the non-singular matrix theorem, although I'm leaving that as an exercise to the viewer here to finish the proof of that. What I wanna do in this video is talk about some consequences here. What type of information will guarantee that a matrix is non-singular or singular? So for example, suppose we have a three by three matrix over the complex numbers and suppose we know its nullity is equal to zero. Can we say anything about it being singular or non-singular? Well, the nullity, remember, the nullity is gonna be the number of non-pivot positions, non-pivots, which in contrast, the rank of the matrix is gonna be the number of pivots. So one thing we see very quickly is if you take the rank, the rank is just gonna be n minus the nullity right here. So that is if you take away from the number of columns, the number of non-pivot columns, that'll give you the number of pivot columns. But if you take n, take away zero, this is just n, and like we saw on our list previously, it was somewhere there, searching, searching, searching, aha. We saw this right here, condition 11, the rank of a matrix is n, which implies that it's non-singular. So if your nullity is zero, that means your rank is gonna be n. And so we can definitely say that this matrix is gonna be a singular matrix. And I mentioned n right here, this would specifically be the number three. But the fact I told you it was three, but three didn't have much bearing because it said n by n. The fact it was over the complex numbers made no difference whatsoever. Let's look at another example. Suppose this time a is a five by five matrix over the field z two. And furthermore, let's assume that the equation ax equals zero has eight solutions, which is possible. Now it suggests that the null space of a is a three-dimensional subspace of z two five. All right, what does this say about singular versus non-singular? Well, this one we actually talked about on the previous slide, whoops, not that slide, this one. We chat about this one that if the homogeneous system has only the trivial solutions non-singular, but what we see right here is that there's eight solutions. So there's gonna be seven non-trivial solutions. So this tells us that, okay, ax equals zero has non-trivial solutions. And so what that implies to us is that this matrix would be not non-singular. So that tells us it's singular. And this follows by the non-singular matrix theorem. Let's do one last one. Suppose that a is a two by two matrix such that a times the vector one two is equal to the vector one two. What can we infer about this? Is this matrix singular or non-singular? Well, it turns out it depends. In fact, we don't have enough information. There's not enough info right here. And why do I know that? Well, because there's actually two possibilities. We could take a to be the identity matrix, right? Notice the identity matrix. If you times it by the vector one two will give you the vector one two. And this would give you the identity matrix is non-singular. So it certainly is possible that the matrix could be non-singular. But on the other hand, we could take a to be the matrix one zero two zero. Consider that one for a moment. If you took this times a, you're going to get one two right here. I'll let you verify the arithmetic right there. But if you multiply one two by this matrix a, you're gonna get the vector one two. But on the other hand, this matrix is singular. How do I know it's singular? Well, look at the column of zeros right here. The column vectors of this matrix a are going to be linearly dependent because the set of vectors has a zero vector in it. And if the column vectors are linearly dependent, that implies that the matrix would be singular. Cause the non-singular matrix theorem told us that to be non-singular, the column vectors have to be linearly independent. So dependent would imply singular. And so we don't have enough information to answer this question right here because with the information provided the matrix could be singular like the one provided right here or it can be non-singular like the one provided right here. So we don't have enough information to nail down whether it's singular or not. And so that's gonna bring us to the end of section 3.3 about matrix inverses, but that does not bring us to the end about our conversation about inverse matrices. What we've done here with this conversation of the non-singular matrix theorem is we've learned ways of identifying when a matrix has an inverse and when it doesn't have an inverse. But when it does have an inverse, with the exception of two by two matrices, we yet do not have an algorithm to find what that inverse is. That will be remedied in the next section 3.4. We're gonna introduce elementary matrices as a tool to help us compute the inverse of a non-singular matrix. Thanks for watching everyone. If you've been learning things in these videos, these lecture series, please hit the like button. If you wanna learn some more cool facts about linear algebra or other math videos feel free to subscribe and always if you have any questions on any of these videos feel free to post your questions in the comments below and I will be happy to reply when I can. Have a great day everyone. Bye.


Welcome to Dispatchers from India, a show by people's dispatch where we bring you major news stories from across the country. As the coronavirus pandemic continues to spread across the world, the governments are rushing to save the corporates. But the crucial question is, what about the millions of workers, permanent, contractual and informal? According to the International Labour Organization, more than 25 million jobs will be lost due to the pandemic. In a country like India, where a large number of workers are contractual and informal, the lack of support from the government will be disastrous for the working class. Apart from the issue of livelihoods, many contractual workers who are involved in sanitation and security services are in the direct line of infection due to lack of proper protective gear. We take a look at the issues of contractual workers involved in the hospital and transport sectors. The number of confirmed cases of novel coronavirus in India had surpassed 270 with thousands under isolation and quarantine. Even if it may seem like India has been able to cope with the rising numbers, experts believe that the growing pandemic will soon break the back of the country's fragile healthcare system. Already, many public hospitals have complained about the lack of personal protective equipment like masks and gloves. While the supply is being augmented for the healthcare personnel, workers employed in sanitation and security services continue to expose themselves owing to the shortage. I work at a government hospital. The in-charge of the nurses there said that all first guards should be given masks. But no one was ready to give us masks, saying that they don't have any. The COVID-19 patients who are foreign nationals have been told to take all safety measures. But then one nurse said that what about these poor people who are working here? Where will they go if something happens to them? They are here to earn their livelihoods. She said to give us masks and sanitizers. Every morning I was asking for this protective gear but they weren't ready to give us masks or sanitizers. How will we raise our kids if something happens to us? These people keep saying that they are running out of supplies. You tell me what do we do? Who do we go to? Then one day the person in charge of distributing masks was doing the rounds at the hospital when she saw that a guard is not wearing a mask and has to touch the door every few minutes. Then she said that the guards are also workers, give them masks and sanitizers. She demanded to know why the rest of the staff was being irresponsible. She complained to another in-charge. Then from the next day we were given masks. We were given masks yesterday finally, one month after making repeated demands. I am a worker at Kalawati Hospital. I am a sanitation worker. We are not issued any masks. When we go to the ward we are told to take the masks from our duty stations. Even for the gloves they tell us the same. There are a lot of workers without boots or any protective uniform. We somehow manage to arrange masks and other protective items from here and there. There is no proper provision for hand wash. There are dead all soaps for us but they are never issued to us. Even the case of hand wash is same. For doctors the government has issued 300 rupees for nurses 200 but there is nothing for the sanitation workers. We do the cleaning, we are also exposed to the infection. The coronavirus pandemic which the world is witnessing has also reached India. Looking at this, the government and the Delhi Transport Corporation management should have taken precautions in the beginning itself and should have issued personal protective equipments to the workers whether they are masks, gloves or cleaning materials. These should have been provided. Despite requests from our union to the government and the management, these equipments are not being provided to us. Both DTC driver and conductor are at risk. A conductor has to give tickets and take money from thousands of people in a day. This creates a big risk for the spread of infection to the conductor and the passenger. The government and the management are doing nothing on this. The drivers without masks are also exposed every day to the threat of virus as commuters pass near by him. There is a risk of the spread of the virus. This endangers the life of the DTC worker and also everyday commuters. When we talk to these workers, they were on their way to the Labour Commissioner's office for their case regarding non-payment of their wages. Later they were turned away as the office was closed due to the pandemic. Some of the workers have not been paid by their companies for more than a month. Courts in India too have reduced their working and are taking up only urgent cases. But according to workers, their cases for wages and other rights are not part of the urgent cases list, nor have the labour courts devised any provision by which these cases can be heard using video conferencing. The workers raised an important question. If the courts will not hear them, where can they go to seek justice and who will safeguard their rights? Today was our court date, it is 19th March. The company in which I work, haven't paid me salary for more than a month, came here at the Labour Court for justice. But here we are only getting days. We are not even allowed to go inside the court because of the coronavirus threat. We also speak to news clicks editor-in-chief Prabir Purkayasta on the spread of the disease and India's strategy to cope with it. As far as the COVID-19 cases are concerned, India still has not reached the danger zone, so to say. But the numbers are creeping up and we really cannot say what the extent of the epidemic is in India without more extensive testing. So at the moment the numbers seem to be that it is in the range that would still seem to show it is within the communities. It can be contained through contact tracing, looking at who are the people who have come from outside. You could have brought in infection, their contacts, tracing the contact who already tested positive. So that's the scene we are in. But it is also true to repeat that and getting over to a community spread when you don't know who is infected, who is really a tipping point, which is difficult to figure out. So at this stage we need to do more extensive testing, random testing, testing of patients who have tested positive for pneumonia and check whether it's actually COVID. See what the doctors are saying in their symptoms, which appear to be COVID-19 like the test them as well. This is one set of testing we need to do and the other hand we need to really increase social distancing and that is perhaps the only measure that we have. But at the same time we have the problem that the number of test kits we have is small, there seems to be only 100,000 test kits, therefore it's been conserved and therefore extensive testing is still not possible. We are looking at getting a million test kits into India, but we don't know when that's going to happen. Manufacturing still some way off. It comes also to the second set of issues that if there is such a large scale of social distancing, what is being called the people's curfew and all of these measures, then a country in which the economy rests a lot on casual workers is going to see a huge dislocation. Where will the casual workers go and what will be their daily wages on which to live. So this is what calls for immediate government intervention. The left government in Kerala has intervened and has made available people, rations available to people, some support, financial support to be given, children to be given, school needs and so on, which is what the schools used to do earlier, sending the rations to the houses. So all of these are measures to see the casual workers on whom the large part of the income rests don't starve because of the so-called people's curfew. So I think all those measures require the third measure, which is also equally important, that how to strengthen the hospitals. In India already, the hospitals are trying to say they don't have enough protective gear. So the government has to have the task of flying immediate supplies to all the hospitals, getting in the supplies to the country by which you have masks, you have protective gear, and it's not only for the doctors and nurses, but the entire support staff of the hospital. And that means those who clean the hospital, who run the hospital, do the auxiliary services, give food to the hospital patients. So a lot of other people are also involved and really all of them need to be protected because if they get infected, then the hospitals also become a source of infection. In our final news item, India witnessed a curious development this week. When a former Chief Justice of the Supreme Court, India's top court, was nominated by the president to the upper house of parliament just four months after his retirement. Observers argue that Ranjhan Gogo's appointment is not just unprecedented, but bodes ill for the independence of the judiciary. We spoke to senior journalist Paranjoy Guha Thakurtha on the significance and dangers of this appointment. In India, politicians have become judges and judges have become politicians. But the decision of the president of India to nominate the former Chief Justice of India, Ranjan Gogo, as a member of the Rajya Sabha, the upper house of parliament in India, that too within four months of his retirement as Chief Justice of India has resulted in a huge controversy. The government's critics have argued that Mr. Gogo has been given that post because he's given his headed benches of the Supreme Court of India that have given a series of judgments that have favored the right-wing Hindu nationalist ruling regime in India. Mr. Gogo, of course, says there's nothing wrong. There's no quid pro quo that this is almost in the normal scheme of things he's been nominated as a judicial expert. But many would argue that there is much more than meets the eye. That despite the fact that in the past other judges have given judgments that have favored the ruling regime in the hope of post retirement jobs. Mr. Gogo's case is particularly unique. Why? Because it was given barely four months after he retired. Secondly, the kind of judgments that were given by the Supreme Court at the time when he was heading the Apex Court of India, the series of these judgments were so obviously in favor of the government that political commentators have gone to the extent of describing him as a virus in robes. Now this has obviously not been liked by spokespersons of the government and they've given dozens of examples in the past of how previous governments have actually done help judges or given judges impressive, ornamental, sometimes even lucrative post retirement jobs. But a strong argument can be made that this decision has undermined the independence, the autonomy of the judiciary in India, which is seen as perhaps one of the last bastions where ordinary people can hope for justice. That image of the Supreme Court of India has been terribly undermined and compromised by Mr. Gogo's nomination as a member of the upper house of parliament. That's all we have today in this episode of Dispatches from India. See you next week. Thank you. Bye.


Good Sunday morning everybody, as you can see him in the car Technically still morning. Anyway, I'm all suited up and we're in the car We are actually running a few masks to a neighbor in need I have extras and they will work for her. So we're running that over there like I might be sewing this afternoon because she needs masks too and Then we're gonna probably stop at one see if they have Lysol or Clorox wipes I doubt it, but we'll probably do that on the way home The main thing is we're taking husband's car out for a spin if you'll notice the inside of the car looks different We're in the husband's sports car. It hasn't been driven in a month. So it needs to be Yeah, it's a little different than driving a Subaru So we're on the back roads. That's why the camera is about me. My arm is shaking And we're driving it around and yeah, just you know doing the social distance thing but Doing it in the car. So all right, I'll be back. So you hear that? Little frogs late. I don't know what time it is It's we are it's well after eight o'clock. I Don't think it's nine o'clock yet. But anyway, we are headed out to get some walking in Before it gets any later and any darker Anyway, so we're gonna go get some steps in I'll see if I can get a few pictures and I'll be back This time it's light outside I haven't vlogged all day But I made a bunch of head tubes today making some more of the surgical style masks tomorrow and the Filter pocket masks on a Wednesday getting a lot of friends and family that need them Some working on that Also made another Zombie doll Corona virus zombie doll I don't remember now if I Shot footage or not at the moment, but also it's a picture of the finished doll right about here. What was the name? Mr. TP shortage It was pretty cute Right he kind of did yeah, we had a TP mohawk Anyway, we're gonna go for a walk and get some steps in of course. I'm protected as it should be and Yeah We'll get it done right all right. I'll be back.  Let me close the doors temporarily. I do want it to come clean in here But hang on the noises a little Didn't cut it out completely but less a lot less. Anyway, it is Tuesday morning It's before 10 a.m. I don't know what time it is. It's April 7th. I think let's go see Yeah, April 7th So yeah, I'm going to I already made some homemade hand sanitizer that was the second thing I did today I fed that sourdough starter. I'm trying I'm creating a new sourdough starter. I haven't had one of those in years So anyway My daughter wants to learn how to bake bread so And at times bread is hard to find at the grocery store fun fact so I'm going to make some sourdough starter. So I'm feeding it. We're on day two of probably like day 14 Although I probably won't wait for two full weeks to cure it to make bread instead of tossing some of it out When I go to feed it, I will probably Make bread We'll see what happens. Anyway, as long as I have flour because that's a thing I'm going to make a bunch of masks today I don't know if I'm going to have time to do another zombie doll today, but we'll see and I will put some pictures here of the current collection of zombies and I have to add a couple of words to the positive affirmation doll that I'm creating for my deacon submission inspiration so Yeah, all that I am supposed to have a telehealth physical therapy appointment this afternoon But I'm thinking of Canceling it and rescheduling it for a couple of weeks out. There's a lot to do around here plus my knee is kind of sore I've been doing a lot of walking And I'm not sure so sure I need one more visit. So I think I'm going to cancel my appointment today and That's it mostly mask making. Oh joy. Oh, and I have to edit the vlog for tomorrow last week's vlog I haven't done that yet. So all right, I'll be back. Okay 19 More cloth surgical masks done. I'm gonna do filter pocket masks tomorrow. I have an epilastic for one more mask So next is robbing the elastic cord and hair scrunchie things out of the bookbinding basket Which I may have found something that'll work. I don't know. We'll see I guess anyway, I'm gonna get the mail and bring the garbage can in and Then edit the vlog, I guess. All right, I'll be back. Hey guys, we're out for our evening walk You'll notice this time. I have a disposable surgical mask on I Am finding when I'm walking I Need either the head tube or one of these on Because I get too hot under the fabric one So if you're still trying to get some exercise in despite the fact that you need to wear a mask You might just think about wearing a thinner mask if you're getting your exercise in Where you're able to easily for the most part maintain good social distance and this is just secure at light security You might just think if this is a little bit better or the head tube Anyway We're gonna try to keep Lily from eating the grass Uh-huh Evidently shelly does it with us. I don't know if I believe that That's what the kids say anyway maybe Anyway, we're gonna go get some steps in and we'll be back. Hey guys, it's Wednesday, April 8th It's like 2 30 ish. I think it's just slightly after 2 30 He spent the entire morning sewing again. I made a bunch more masks And I'm sending three of them off to a cousin who needs them And I've got a bunch more now for anybody else who asks in my family I keep giving them all away. So anyway Um, I'm going to I ate lunch. I'm gonna try to squeeze this in the mailbox. Hopefully it fits and Then I'm gonna Either work on something new I've just discovered called slow stitching or make another voodoo doll or something It's a beautiful day out. It's nice and warm. I've got the windows open I didn't enjoy what I can while I can right? All right, I'll be back. Hey guys We're out for an evening stroll with my mask on One thing that we're noticing and every this is the second time recording this by the way. I forgot to hit the record button the first time anyway huh take two One thing we're noticing being home from the pandemic Because we can't go out like we used to we can't get the convenience foods we used to I'm doing a lot more cooking which I haven't done in a long time Uh, that's why flour is always gone At the store and sugar and all that stuff so I took some Supplies that we had on hand including some organic honey from a friend in california What was it go for gulch? Yeah, we'll We'll we'll find a social media or something link. We'll link it below. We'd love her honey. Uh, she she's a beekeeper Anyway, I made a sourdough starter with the honey instead of sugar I started it on sundae I split it into two jars today And it wasn't quite ready to bake with But there was a little bit left over. I didn't want to waste it So I made the first loaf of bread. Oh my god. Was that good? Why did I split it into two jars? So when my daughter and polies get to move into their house, they have their own Because she wants to make bread Anyway, first loaf of bread made in like 10 years or something So anyway, we're gonna go get some steps in now Because I ate a couple pieces of bread and you know Yeah I also spent the day doing some More masks. I'm done with that for a bit Organizing some other things so I can do some more voodoo, uh, zombie dolls, not voodoo dolls, zombie dolls and um Uh Then I work on Playing with some slow stitching If you if you guys out there do that, let me know I'll link some references that I can find in the description I just Discovered it.  All right, so This would be why my allergies have been going haywire. No, it's not the corona This is the hood of my car It has so much pollen on it Like the whole thing look at this My car and my Bob just had the car washed Over the weekend on sunday It's like this like it's almost like there's layers snow on it. You just they not that you could tell it's been cleaned recently It looks like I haven't driven in two months which isn't Too far off the mark. I haven't driven it but family members have and it wasn't this dirty. That's just gross Anyway, stay safe. Stay home. Stay creative See you. See you later. Good morning. It's 10 o 8 a.m. Ish Thursday, April 9th, I think Yeah, anyway, I'm headed out to get the mail. It's here early Haven't done much yet today But I plan on doing a lot of sewing and stitching so We'll see how far I get. I'll be back. All right So it's just a minute before two o'clock and I got my zombie doll done for today. I'll put a picture here It's mr.  My sister Elizabeth lost her job because of the coronavirus Um, it's one of many that I know that that's happened to you right now Uh, I know a few people that are sick with the virus I wish them well and I wish them a speedy recovery and for them not to end up in intensive care because that would be bad um What else? I want to work on some slow stitching, but I think I'm going to take a break and eat something besides wheat thins and Yeah, go downstairs and maybe actually have some lunch something with a little protein in it even if it's peanut butter And maybe take some sausages out for dinner All right, that's it for the moment. I'll be back. Hey guys. Good morning. It is Friday April 10th I think I don't know what time it is, but it's still morning. I don't think it's 10 a.m. Yet um I'm still my pajamas I need to take a shower. I have already been up and checked social media and Uh fed the sourdough starter. I am making another loaf of bread The daughter's off to do the grocery shopping for us since I'm in the vulnerable category and Try to get that done. I did have Polyas text her and ask her if she can find it. Can she get all-purpose flour? I don't know if she's going to be able to find any, but um We're not in desperate need yet, but you know the jar's half empty. So start looking now um Got the last of my laundry out of the drier I need to fold and start and put things away. I need to clean the house today So this is going to be just a day of chores. I don't think I'm going to get any or much art done I'll probably be lucky if I can sit down and finish reading my slow stitching book But we'll see and I do have a couple more ideas for Zombie dolls. So I want to write them down before I forget. So I guess I better get dressed and get to it, right? All right, I'll be back. Okay, both of the downstairs bathrooms are clean the kitchen is clean All the pollen is cleaned off of the surfaces in the art room I'm To really pollinate out and we had the windows open and just it blew right in the house now. I'm coughing. I know Add some lunch. I'm gonna just relax for a minute before I do anything else. All right, I'll be I don't think the boys get that lily is never going to figure out what baseball is I I don't think so We're gonna end somebody's gonna end up getting hurt Dad dad probably yeah, probably dad He wishes he was young enough again to play baseball He'd hurt himself Why do I have a feeling we've gone off on a trail? We're not really supposed to be on Yeah, that's a thing Just run down I can technically say good morning everybody because it's 11 11 33 a.m Saturday, April 11th day before Easter um It's gonna be a weird Easter anyway Um The family helped me get the house clean this morning and do all the dusting and things since We're doing our part and staying at home and staying isolated and You know our lady who helps me get to keep the house clean is not coming in for obvious reasons Hello If you're watching this in the future research 2020 and the pandemic and you'll figure it out um Anyway The family all had things to do today But I made them all promise to help me get the house clean which they did so the house is all nice and clean and spotless And if you hear a motor-ish noise in the background there is My daughter and future son-in-law have a rumba and it's Doing its thing upstairs Hope it's not stuck. It sounds like it's banging into something um Anyway, so it's doing its thing I just finished feeding the sourdough starters. You can oops see them on the counter behind me I maybe should have took taken some more out today and then fed them. I didn't So I guess we will kind of see if they overflow later I might have to let them like get near the top and then punch them down and let them Rise again I'm definitely gonna have to cook rolls or bread more bread or something tomorrow So, yeah, that's a thing. Um, I'm gonna go upstairs and Fiddle around on the computer a little bit. Um, I need to work on my recipe binder that's down here because I've just been shoving stuff in it for like a long time And I think it's time to put The recipes I know I'm gonna want to cook again into protective sleeves and put them actually in the binder So that things aren't falling out every time I pick it up because that's a thing Anyway, Lily is here. She's outside. She's kind of upset that she's home alone with me She prefers all of her people to be at the same place at the same time um So, yeah, that's a thing She's not in the backyard. I think she's looking for snakes. We have garter snakes red striped garter snakes Okay, that was a giant pain. So I got all my recipe clippings sorted and organized and my smaller recipe book redone.  Thank goodness for The cable. Where are they? These cable binding wire things. I'll link them in the video description. I got them from amazon and book binding tape Made a big giant mess, but I got it cleaned up Onto the next As I'm turning the phone the camera on on my phone to close the vlog my husband's complaining about how the street and everything is all yellow Everything is covered in pollen On top of everything else that's going on in the world We're having like the worst pollen season on the planet anyway, I Didn't think I'd get a whole lot of like art stuff done, but to my surprise I did get another zombie doll done. This is misinformation. I'll put a picture here I got another word on my positive affirmation doll done create put that here And I also got a couple of more drawings done in my daily drawing journal. So I'm surprised Anyway, we are headed out to get some steps in And uh, yeah Lily's doing her business so her business yay Anyway, we're gonna go get some steps in I probably should have a sweater on it's a bit nippy, but it's not too bad I don't have a sweater. I know it's probably I'll probably be hot before we get home anyways, so Lily come here. Lily no grass sit down sit Sit Anyway, we're gonna go get some steps in We hope that you guys have had a good week And been able to muddle through with our new reality That we're all trying to deal with Got a muddle right there Anyway, uh, stay safe Yeah, stay safe. Stay healthy. Stay creative Don't forget to check out the video description out for ways to support the free the free content here on youtube Go toss it down there Anyway, sorry Don't forget to don't forget to check out the video description For ways to support the free content here on youtube and if you have a favorite creative on youtube They probably have ways that you can support them in their video descriptions. Also Also on fapes facebook a lot of the creatives over there to do also So if you can't find information for a paypal tip jar or an Etsy store Or patreon or something ask them email them and ask them Message them make a comment on their video because I bet there's a way And we would all uh love your support, especially in this time When you know Holy cow Anyway, uh, don't forget to like share and subscribe and the most important thing Go out and do something nice for yourself because you deserve it Even if it's just in your own backyard because you're in quarantine All right, that's it for now. See you next week. Bye guys


Manny, how were you able to balance the use of your pitch mix over the first two times facing that line-up? Yeah, that was the idea tonight, you know, to mix all the pitches, you know, especially in attack counts and in the zone, you know, and establish confidence early. And, you know, that was the plan from the get-go. What kind of confidence do you build when you're able to essentially back pocket your best pitch, your change-up for when you really need it?   Aaron Boone has been saying you made some progress down the trip away, but we see the ERA was seven down there. What was going on down there? And while you were giving up some runs, did you feel like you were making some corrections on things? Well, I've been working on it, I've been developing it, and it's already done, it has taken, it has progressed in development as a launcher, although perhaps the effectiveness is a bit high down there. But what are the things that you've been working on down there that have allowed you to launch better? Well, down there I'm working a lot with my location, the sink, out and in for the batters. The exchange is trying to use the lower areas and the slider, which is the pitch that is helping me a lot in my career. And I'm still working on my corrections.  I used the sinker to both sides of the plate and keep the change up low in the strike zone. And as I mentioned before, I've been working on a slider that has been giving me really good results and polishing that pitch down there, putting a good package of pitches has been the focus. You mentioned the slider a couple of times. How do you like your slider compared to your curveball right now? Which one do you feel more confident in? You know, by mentioning the slide several times, there are some that you like the most about the curve slide, one, as one uses it, one to the other. You know, I use the curve map with the attack to the south. It also depends on whether there are right-handers that are weak with curves. I can also use it, but I use it more for the south batters, with the attack, with those that have the same tension, I can use it with any counter because I trust the curve a lot, but the slide is a pitch that has helped me a lot with the right-handers. Yeah, the slider really has been using it more against righties and the curveball for lefties. You get a pretty good idea who's a lefty hitter that you can use the curveball against. That's how you break down the usage, depending on the opponent. And how do you feel about being called up here and realizing you're up against an accomplished pitcher like Castillo? Yeah, it's a great opportunity to face a guy like that. He's one of those stars of this game. At the same time, I've got to go out there and do my job in pitch, so good experience.


Before we get into the video guys, if you guys want to be with a chance of winning this resurrectionist emblem, leave a like and tell me in that comments section what you're most looking forward to from Destiny 2. Can we reach 4000 likes? That'd be absolutely epic if we could. What's going on guys? Today I bring you another Destiny video and today I want to talk about the new Age of Triumph treasure packages, the treasures of the ages. So what do these contain? Well actually they contain quite a lot of goodies, although mostly older items which you may have missed out on from previous events, but they also contain some new things too. So firstly, the older things are obtainable. Ok so if you are missing certain armour to complete older collections like the Spectre armour, the Desolate Taken armour, the Dawning armour or so on, these packages have a chance of dropping what you might have missed. But it ain't just previous live event armour you can obtain from these packages, you can also obtain them old Emblems, Ghost Shells, Emotes, Festival of the Lost Masks, Sparrow, Sparrowhorn, Chips, basically everything. You can also obtain the days of Iron Ornaments to apply to that Iron Lord gear if needs be. Also obtainable are all of the consumables previously obtainable from previous live events as well as Chroma and that is basically all the older things obtainable from these new treasures of the age packages. So what about new things? What can we get? Ok so across the board there will be new armour for all three characters. We haven't seen what it looks like yet but I do believe they promised within next weeks third and final stream it will be showcased to us. As well as this new armour there are also seven new exotic weapon ornaments coming too. We have one for the Nolland Beyond, the Necrolcasm, the Vex Miforclas, the Touch of Malice, the Dragon's Breath, the Lord of Wolves and the Surus Regime. Now I'm pretty excited to see what these look like to be honest I'm not going to lie. So as well as these new armours and exotic ornaments there are also two new ships obtainable and three new shaders. The ships are called Order Theory and Needle and Thread and shaders are called the Blast of War, Barrage and Brush of Fire. So people those are the contents of these new packages. We can see that the first two sections are guaranteed items from this package but all the new stuff there's only a chance it will drop, not a guarantee. So more about these packages, how do we obtain them? Well there are two ways, grind or pay. So to grind for them you have to complete three of the featured activities within the weekly rituals. You get one per week from the Sea of a Crisis or Oak playlist, one from the Weekly Story playlist and another from the Featured Weekly Crucible playlist. Now you can only obtain three per week across all three of your characters. You can not obtain any more it seems, unless you want a part with your money, that real life dollar dollar. Now as always I have no problem with people spending their money on what they want as I do the same thing I buy these packages basically with every live event. What pisses me off though a little with this one is the fact that because there's so many obtainable things from these packages now it means you are less likely to get the things you need meaning you'll spend more money to get items you desire but that's just my opinion. So guys there you have it, the treasures of the ages and all obtainable items from them will be obtainable on the 28th of March when the age of triumph hits. Hope you guys enjoyed the video, thanks for stopping by as always, subscribe for daily destiny, turn on the bell notification so you never miss a video and I'll catch you on that next one.