5

H H(a)(4)H A HH HHH~HHHH ZhHHCH;...

Question

H H(a)(4)H A HH HHH~HHHH ZhHHCH;

H H (a) (4) H A H H H H H ~H H H H Zh H H CH;



Answers

(a) $\mathrm{F}_{1}(\mathrm{a}) \mathrm{F}_{1}^{\prime}(\mathrm{a})+\mathrm{G}_{1}(\mathrm{a}) \mathrm{G}_{1}^{\prime}(\mathrm{a})$ (b) $\mathrm{H}_{1}(\mathrm{a}) \mathrm{H}_{2}(\mathrm{a}) \mathrm{H}_{3}(\mathrm{a})$ (c) $F_{r}(a) G_{r}(a) H_{r}(a)$ (d) 0

We have B over H equals L times W. And we're solving for h I'm gonna take a Church Times. L.W. Equals B. Times one. So we equals L w H. So now L W is being multiplied by age, so I'm going to divide by L W. Okay. And now I have the E divided by L W. Yeah, equals each.

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

Okay, So for part eight, this is going to be a two by two matrix or he is going to be a three by three matrix parts. He's like to be an undefined on defined because it's simply not possible harpies going to be a two by three Matrix party's going to be three by two Matrix Heart F is going to be a three by three matrix, part G. The party's also going to be undefined, but it's simply not possible. Undefined on party. I don't know howto do off its top party. Her H is going to be a three by two matrix.

In this problem, we have to evaluate the limit Limit Edge approaches zero sign nine edge over sign seven inch. Now we know that trigonometry limited when limit theater approaches. Zero. Sign theater over theater is equals to one. Therefore, limit edge approaches. Zero Sign nine age or sign seven Age is equals Toe limit H approaches 0 9/7 Multiply sign nine edge over nine inch and seven edge over sign seven Edge, therefore simplifying eight. We get limit edge approaches. 0 9/7 multiply sign nine edge over nine edge. Multiply one over Sign seven. Edge over seven edge. Now applying the techno metric limit, we get nine or 7. 45 1 medical one or one. Therefore we get 9/7. Therefore, limit edge approaches. Zero sign nine edge over sign. Seven Edge is equals Tau 9/7. So the final solution is this one


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