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Bpt X 0 01 XC 'h 22"swuole uabaxo zzOI X S"v suiejuoj 1e41 suej? ul%(hHOJe)Jo ssew a41 a1einjie) :s,oupeBoAV SajoW ssew :T OapIA BUIMOIA Javyv

Bpt X 0 01 XC 'h 22 "swuole uabaxo zzOI X S"v suiejuoj 1e41 suej? ul%(hHOJe)Jo ssew a41 a1einjie) :s,oupeBoAV SajoW ssew :T OapIA BUIMOIA Javyv



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$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CONH}_{2} \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}$ Here $(\mathrm{X})$ is (a) $\mathrm{Ni} / \mathrm{H}_{2}$ (b) LiAlH $_{4}$ (c) Zn (d) $\mathrm{Pt} / \mathrm{H}_{2}$

Ah, good day. This is question number 22 and we're looking at the vectors accent. She and Wyatt t here. And in this case, I didn't really bother writing down the whole problem. You can read it off, but basically, there's a few stuff to this. And the 1st 1 is to look at whether or not exit e and y of tea. Barb, a fundamental solution said for the homogeneous, homogeneous linear equation, X prime equals t a X. Um Okay. So, again, I don't you They used a notation x one x too, but I just used excellent. Why? Which is a big deal, I guess. But still, um Okay, So since exit t and y of tr to actors meaning they're two dimensional or to have two coordinates, it is enough to check the ron skin. And in this case, um, so the wrong skin is just the determinant of this matrix. And, um, you know, if you do the algebra again, this is a two by two matrix you should buy. No. Now know how to calculate the determinant of this? Ah, you end up with negative Clyde E to the three t and that you can check that w zero is not zero. It's in fact, equal to negative five, meaning that Exit E and Y a T form of fundamental solution said Okay, so the first answer is yes, they do form. Ah, fundamental solution. Set. Um, and the accept being the fundamental matrix is exactly this guy here. This is your fundamental matrix. The definition off the, um, Ron ski and, uh comes from the fundamental matrix. Okay, so the final question is toe thio. Find the general form of solutions. And to that end, this here, uh, Z f t is a general solution, general form of solutions. And, um Well, I just, um you know, if you if you wish, you can write the, uh like this, but I wouldn't it this is just simplifying or I don't know. You even know if it's simplifying, but actually computing. Um, this z of two I don't really think of it is simplifying anything, but that's what it is. So Okay, so that's your general form of solutions. So, um, just, uh that's the answer to your question. Uh, thank you.

This video, we're gonna go through the answer to question number 11 from chapter 9.4. Where we asked 03 Why? To rewrite this matrix equation in normal. So they're all the other three by three major cities or 33 dimensional contractors. So let's let thanks the back to X. Hey, three dimensional color factor. Thanks. Why's that? So there are three components. They're looking for three differential equations, so just read them off. So the 1st 1 it's gonna be ex prime of equal to So looking at the top row off the three by three matrix, it's gonna be one x There's gonna be no wise, and it's gonna be one that there's gonna be long times easier t on nor Times two. Next up. Why crime is gonna be his minus one X plus two. Why plus five. Is that close? Zero time. These a T was one times t finally said prime gonna be equal to zero loss off x five. Why is one well off set on DDE? That zero loss off eats the tea on dhe There a lot of tea. So this system off difference the questions is no

In this video, we're gonna go through the answer to question number 35 from chapter 9.3. So it has to show that the Vector X, which the function of tea is a solution or rather satisfies at the system the differential equation system given here. So, first off, we wanted to find the derivative of thanks its function of tea, So just do this. Each of the elements. So that was over. The top element is three e to the three. T. The bottom element is two times three, just six, eight and three t. Okay, Now let's find what the right hand side is. So that's one one minus two for times by X. As a function of tea, this is gonna be the matrix 11 minus two, four times by eater three t two you to the three to. So this is gonna pay each of the three T plus two eaten three T, which is three e to the three t in the time element on the bottom element is gonna be minus two eaten sweetie plus eight, which forced us to a three d so minus two plus eight is plus six Hey, so the three t which is exactly what we found when we took the derivative off X has dignity. So yes, the vector were given to satisfy

First of all, let's come third, the director off x t. Grisham Youth is so wreak a easily calculator to these words you called Chu zero. You keep all our next to history the cheap hope for Let's calculate. So he's well, not tricks. And there's the ex magics. Yes, you call Choosy are old then power. There's 2 to 3 each power we calculus Is the products off of these too Magics So there as there will be zero Oh, people were next. 23 You keep hold or and we can see the answer. Yes, he called truth the directive off x ext even motion So we can see so venter ext t satisfy.


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