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Find matrix such Inai AX -BFind ? matrx Guch thalAX 2 Solect Iha co recl choke balow and nacassan_anaalcomialato YOUI choica0 B. Tha mutIx h nol invorublo und thato...

Question

Find matrix such Inai AX -BFind ? matrx Guch thalAX 2 Solect Iha co recl choke balow and nacassan_anaalcomialato YOUI choica0 B. Tha mutIx h nol invorublo und thatoforo tnoto no mutiux XCilck t0 solacl and enter yaur ansvrers)

Find matrix such Inai AX -B Find ? matrx Guch thalAX 2 Solect Iha co recl choke balow and nacassan_ anaal comialato YOUI choica 0 B. Tha mutIx h nol invorublo und thatoforo tnoto no mutiux X Cilck t0 solacl and enter yaur ansvrers)



Answers

Find (a) $\operatorname{det}(A),$ (b) the matrix of cofactors $M_{C},(\mathrm{c})$ adj $(A),$ and, if possible, $(\mathrm{d}) A^{-1}.$ $$A=\left[\begin{array}{rrr} 2 & -3 & 0 \\ 2 & 1 & 5 \\ 0 & -1 & 2 \end{array}\right]$$

All right, so here we are, given a matrix a 100 x 10 zed. Why one? And we're told that a squared plus 0 +00 negative. +1000 Negative +10 is equal to the three by three identity matrix. So we need to figure out what x y and Zed are. So the way that we can do that is first, let's figure out what a squared is. So a squared is gonna be a times a which is going to be I'm just gonna copy these guys down. Uh, that pasty. Yes. There we go. So only real way to figure out what the square of the Matrix is, unless it's in a very particular form is to do the matrix multiplication by hand. So and the i j element of our product here is going to be the dot product of Roe I from this guy on the left with call on J in this guy on the right. So element 11 21 times one plus x time. Zero places zed time. Zero. That's just gonna be one element. 12 Yeah. Sorry. Actually, I'm gonna go to one zero times one plus one time. Zero plus white times zero Gonna be 0310 times, one plus zero times you're a post one time 00 12 is going to be one times x plus x times one plus that time zero. So that's going to be two X up there element to 20 times x plus one times one plus Why time zero Going to be positive. One element 3 to 20 0 times x plus zero times one plus one time. Zero Just gonna be zero Element 13 is going to be one time said, plus X times Why plus zed times one. So we get to, um So, yes, that would be to Zed. Plus X Y is our element 13 there element to three go t zero times said, Plus one times why. That's why times one that's going to be, too. Why and then element 330 times ed plus zero times y plus one times one is one. So we now need to solve the equation. One second here. So we had a square. Yeah, I'll just copy and paste these guys from above. So the way that we can look at This problem now is that we actually have ah bunch of little equations to use to solve for our three unknowns the X Y and said because one thing that we needs toe have If so, we can check a few things. First of all, that one plus zero is going to give us the one that we need there. That's OK. One plus zero is going to give us the one that we need there. And one plus zero is going to give us the one that we need there. So what? This what is useful to us here is that if we look okay, we'd have to have two x minus one equals zero two X minus one equals zero. Tells us then that two X has to equal one or X as equal 1/2 then two. Why minus one equals zero similarly tells us that why has to equal 1/2 then lastly, we have to zed plus x times y has two equal zero or sorry to zed plus x times Y plus zero has to equal zero. So that tells us, lastly, that to zed is equal to negative. X times Why, but we know what X and y are A to Zed equal. Negative 1/2 times 1/2 is going to be 1/4 Tuesday is equal to 1/4 or a negative 1/4 and said has to equal negative 18

We are given an X matrix and then we're also given an O matrix were simply asked to take the O matrix minus the X matrix. So that means we're taking a matrix of 0000 And we're supposed to subtract that with the matrix of X. Why? See, w So the first question, of course, is Are we even able to combine these Because we know to add or subtract matrices, they have to have the same order. They have to be the same size. In this case, they are both two by two matrices. So that means, yes, we can actually go ahead and combine these. So remember then, once we've established that we can combine these, the way we do that is by combining each of the corresponding entries meaning this zero right here will be taken minus X right here because they're both in the top left. They're both the first term of their of the first row. And the first term of the first column zero minus X would give us negative X. Then we move on. We would take this zero minus. Why zero minus. Why would give us a negative? Why then we'd go down to the bottom row. We take this zero minus this Z zero minus Z would be a negative z kind of starting to see a pattern here. Then finally we would take this zero right here, minus w zero minus. W would be negative. W That would simply be your final answer. Negative X negative Y negative z negative W

We want to use a calculator to find the inverse of a matrix. First we need to identify the matrix or define it. So hit new matrix. I'm using the decimals calculator. Handheld would be similar. Then you have to put the elements of this matrix into your calculator 202 150 -102. Once it's defined, hit enter and then hit matrix a inverse key. And we can say it's a .3 repeating zero negative point to repeating .06 repeating .2.06 repeating .16 repeating 0.2 repeating. You can also change it to a fraction if you wish.

We want to use a calculator to find the inverse to this matrix. So I'm using the desk most uh that's most matrix calculator. I'm gonna hit a new matrix and choose four by four and then input the elements 3100 1310 0131 0013. It enters so that it is stored and then you choose matrix A. And hit the inverse button and you can round those decimals or you can turn them to fractions if you wish. So it's 21 55th negative. 8 50 53 55th negative one 55th negative eight 55th 24 55th negative 9 50 53 50 53 55th negative nine 55th 24 50 58 55th negative 1 50 53 55th negative. Eight 55th 21 55th yeah. Mhm.


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