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Insinuctor-created questonUce StutCninch t0 computa [...

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Insinuctor-created questonUce StutCninch t0 computa [

Insinuctor-created queston Uce StutCninch t0 computa [



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$$14,356-13,253$$

In this video, we're gonna go through the answer to question number 19 from chapter 9.3 to rush to find the inverse matrix off F S R E O X, which is a matrix as a function of time given here. First, let's recall that inverse off a product major sees a B is equal to the inverse off B plans by the invested a sharing all of the investors exists. So let's think about how we can write this in a slightly different way. So we kind of want toe, not have to worry about all the u to the t You need to mine it easy to tease. So let's just write the coefficients first 14 and then you see that all the first row almost quite by eating Timmy on the second row E to the minus t you know, 30 points to t so we can turns up by e to the t zeroes ever in the second row zero e to the minus t zero and 3rd 1 00 each of the two teams. Okay, let's call this one a on. Let's call, this one will be, Then we can use this formula to find the total invest. Okay, so first up, let's find inverse off, eh? Let's do it in the usual reduction way. So what we got 111 one minus one. See? You want one? Combine that with the identity. 100010 There. Is there a woman? Okay, we're reducing. Let's subtract the first row from the bottom room. That gives us 00 three minus 101 less. Attract the first road from the second road zero minus 21 Uh, then screw reminds 110 leave in the first row is it is one warning zeros era. Okay, so try it times in the bottom row by 1/3. We got 001 minus 1/3 zero 1/3. Get me. Okay, then this new bomb row, we can subtract that from the 1st 2nd most. So from the first room gonna be 10 because I want one. That one minus one is zero. It's gonna be one minus a bird. Sorry. One minus minus. A bird, which is one plus a bird, which is 4/3 zero minus 00 zero minus 1/3 as much bird. Then subtract the new bottom row from the middle road is your, uh, minus two zero minus one minus minus 30 miles. Off course, a bird which is minus two birds one minus zero is just 10 minus. The third is my herd. Okay, so bottom row stays the same. 001 Mines third, zero third. Let's multiply the middle Robot minds heart to get 010 Ah, my hard times minus 2/3 is 1/3 then one times minus half is mine minus half minus. 1/3 is 16 Then let's do the top road minus this new middle road. Then we're gonna get the matrix on at the identity matrix on the left for the 4/3 minus. Good. This one zero minus 1/2. It's okay. Zero minus minus 1/2. It's 1/2 on minus. 1/3 minus suit is minus 36 Which is my heart. Okay, so this is our inverse off the function called a Now it's fine. In burst off. I actually called bay. So be waas. Eat the tea. 00 zero. It's the minus t zero. Is there? Uh, zero. He said to take the inverse of this. This is really easy. Um, because when you got a non zero elements in the leading diagonal on and it's just the reciprocal off those beating darknet values on the rest is all zero. So eat the minus t 000 e to the T they were zero zero. Eat some honesty. Sorry. He's the mind to t expended in verse off X, which is inverse off. Maybe. Which is? They invest a inverse, which is, if the modesty 00 zero e to the T 000 into my studio tea. That's our invested. Be invested a waas one, huh? Minus off that, But it's hot. Six minds of the zero Third. Then when we we'll find them together, it's question, but we got E to the minus. See, huh? Modesty minus ah, the money's team. Bird eats the tea. Mine's 1/2. It's the mind. Yeah, it's the team. Six. It's the team, but Murray get minus. 1/3 eats the minus Tootie zero on the third eats the mind stated, and that's I invest

To finding the last class transform of E to the negative to tee times Sign of to see well e to the three tee times t squared Now, using a table this is equal to the laughter show in some of the first, which is to I have a pass plus two square plus for the two Here comes from the negative due here before is the square of two. And this to also comes from this to the lab past Transmit The second term is too over s minus three cute.

Hello, everyone. Today we're gonna find at least the 1st 4 non zero terms of the general solution to the differential equation w prime plus X w equals e to the X. So first, we're gonna write everything in terms of power shoes. So we have w X equals sum over n greater than equal to zero of a n X to the end w prime of X being the sum over are engraved ankle toe, one of end times a n times X to the n minus one, and e to the X is equal to the sum over and great article 20 of ex city n over n factorial. So now we substitute this entire equation so that we get there's some over end greater in Quito, one of end times a n times X to the n minus one plus the sum over all and greater than equal to zero of a n Xidan plus one and that is equal. So the sum over end greater or equal zero of exit e n over n factorial. And now we equate coefficients. So for the constant terms we get a one which is equal to one over zero factorial, which is one for the X terms we get to a two, was a zero, which is equal to one over one factorial, which equals one. This implies that a two is equal to one minus a zero over to and in the X squared term we get three a three plus a one which equals one over to factorial, which equals have. And this implies that a three is equal to negative one over six. So now our solution w X, with at least the 1st 4 non zero terms, is equal to a zero times one minus 1/2 X squared, plus the rest plus X plus 1/2 x squared, minus one over six X cube, plus the rest as we wanted.

You used to fight toward up by the legs then Bernardo, by no way then don't of you. But do is there the function is Do you get a polar? That play? You're saying off heads, remember, you minus does a square. The blue bless work equals zero. So first we need to find affordable by blacks. It is it's number. You you can go available on its way in Dubai. Yes, into the polar. It's like into course it's W India. No, the real. But publics might as that square, I don't know, but Bill s equal to zero. Who if you take the Lord of your bagel X over, they can sort it like why it would about pick flight in beside heads and w they're quit. Why does available are excellent. It go calls head to w be part of the business. When it looked like a big old it'll be like side. It's a w it do into the parlor explain into pigs. Plus, he did a bar X like in tow calls to w you do notably obey bill like, but it does. They're squared and do Dorda bill by it all y equals zero so no w by no lady if your tape calm and we will get like minus side Head said that you know, eggs. You did a lot of excellent David Obey evil about it perfectly into course, hitching a B minus there quick. Then the partner took was noticeable. That break elicit opiate bagels that function real bigger. Can you play? It is to explain in group Cools it's a number you into report a bill, but music minus was that square and that would a bill by Bill. Is it my life rules that equal Brazil? So, Lord of Real Baby Bill, is it Indo here in the bar Exley finger? Because hated Abreu by just is that square tickle toe bruise that w so Berta blew by those that you could do. Who's that? W door. But you dicks to Pixley course. Heads of embryo minus Does that question


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