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Find A(2A) 'euch Inut nulura =6#nonliklulilFind Ihe uwetsc ol Iho olunontar ratrixGanancnthrnentny MatnEC whosd ploduclIha guen nonanigulatMlnm1 1 ]Find an LU...

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Find A(2A) 'euch Inut nulura =6#nonliklulilFind Ihe uwetsc ol Iho olunontar ratrixGanancnthrnentny MatnEC whosd ploduclIha guen nonanigulatMlnm1 1 ]Find an LU-factorizalicn ofthe matfix

Find A (2A) ' euch Inut nulura = 6 #nonliklulil Find Ihe uwetsc ol Iho olunontar ratrix Ganancn thrnentny MatnEC whosd ploducl Iha guen nonanigulat Mlnm 1 1 ] Find an LU-factorizalicn ofthe matfix



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Given $A=\left[\begin{array}{rrr}1 & -2 & 3 \\ 4 & 5 & -6\end{array}\right]$ and $B=\left[\begin{array}{rrr}3 & 0 & 2 \\ -7 & 1 & 8\end{array}\right],$ find: (a) $A+B,$ (b) $2 A-3 B.$

Section 32 Problem 36 against two majors, even A and B tell us that the determinant matrix a minus six and asked us to find the determinate of matrix B. So in order to do that, we need to describe the transformation from A to B. Um, if you look at it, the you've got a D in G only transformation. Going to make that happen is a transposed. So a transpose is going to be a T g and then e All right, on then, be I see. And then you have h and F so that would be the transposed. And then if you look and see what happens, Okay, so if I transpose it first, then the transformations that happened are it looks like two times were one what happens. And then it looks like you see row two minus row three. That's the value that gets into road to. And then it looks like on the bottom you have minus row minus for one prince wrote three that becomes the value in row three. And so what? You see, the transpose, um, has no effect on the determinant. Multiplying by two. Well, multiply the determinant may to combining. Rose has no effect on the determinant, So the determinant of B is going to be too times the determinant of A which is minus 12.

Part eight were considering the vectors we have you in equal toe defector 56 and a equal to the vector to negative one now to find the projection here. So the magnitude of the projection he sub you is going to be equal to the absolute value of you dot product with a over the magnitude. Uh, so this is gonna be what we got, Product. Um, 56 and two negative one. So the absolute value of 56 got it with, uh, to negative one over the magnitude, Um, of a. So the magnitude is the square root off while looking at a we take each component and and we square it the square root of two squared. Plus, we get that some and then square it. So the square root of two squared plus negative one squared the square root of two squared plus negative one squared. Ok, so well, the dot product of the numerator here is gonna give us, um, while we get five times two plus six times negative one. So that's 10 minus six. So the absolute value of 10 minus six over all, the square root of two squared plus native one square That's the square root of four plus one. So therefore the projection here is equal to well, the value of 10 96. Um, that's four over the square root of five. Right. So therefore, the projection here, part A is four over the square root of five. Now, for party, we consider the vectors you equal to the vector three. Negative too. Six. And we have that The vector A is equal to one to negative seven. Okay, now again, from the projection here we take the absolute value of you started with a So the absolute value of the vector Um, you were just three native to six and then that product with 12 negative seven and then over the magnitude of a sets the square root of the sum of the squares of all the components of the square root of one squared plus two squared plus negative seven squared, which is equal to the absolute value of three looks of three minus four. But that's three times one plus negative. Two times two plus six times negative. Seven. That gives us three minus four, minus 42. Right during that product on our numerator, so f value. Um, over. Ah, sorry. Over, um, square root of one squared plus two squared, plus native seven squared. That's the square root of one plus four plus 49 which is equal to where? All the absolute value of negative 43. So that's equal to their for a positive 43. Taking the absolute value over the square root of 54. All right, so there is our answer for party.

Here We got these two matrices A and B. So the first thing that we should do is computer determinant off A that is equal to the multiplication off the elements of the principle of Guyana that is minus five minus and multiplication off the elements on the off Dia that is 12. So this is equal to minus 17. Then we need to compute the determinant off B on that is equal. So this first multiplication is equals to zero. So we need to put minus the multiplication off the element on the other diagonal. That is six. So here is minus six. Then we need to compute the multiplication off a times B. This is equal to 543 minus one times 061 minus two. On this eyes equal to 4. 22 minus one on 20 on. Finally, we need to compute the determinant off this multiplication. But this is equal to the multiplication off the determinants on this is equals to minus 17 times minus six, which is equal to 100 to

So in order to mortar applied, a matrix is A and B. We have to first note that the number off the length off each row in A has to be equal to the length of each column in B. So we know that there's two elements any drove A. And there's two elements in each column A or B, so we know that they can be mortified together. So first success No, start with a and just right out. So one one time zero It will be so the first element off a watch pipe by the first element off Be so one times ever plus to I'm 21 as it's the second element of a on the second element of being these two. And then for the next row it would be free times one plus four lots of zero. And then the final rule would be five times. There are plus six times one and then just cleaning this up, it would be, yeah, A B is equal to to 36


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