5

2222 1 2 1 1 1 U 1 1 03 I 1 7 1 1 1 I 1 1 8 8 3 8 ! 1 1...

Question

2222 1 2 1 1 1 U 1 1 03 I 1 7 1 1 1 I 1 1 8 8 3 8 ! 1 1

2222 1 2 1 1 1 U 1 1 03 I 1 7 1 1 1 I 1 1 8 8 3 8 ! 1 1



Answers

$\left[ \begin{array}{rrr}{-2} & {-1} & {1} \\ {2} & {1} & {0} \\ {3} & {1} & {-1}\end{array}\right]$

We want to use a calculator to find the inverse of a matrix. I'm going to illustrate this with the decimals matrix calculator. So we're going to hit new matrix, identify this as a three by three matrix and then put in the elements 120 which is optional, type -1, -1 2 -10. Want us to find, then you just type Matrix A. And then the inverse. And you can then identify the inverse as 0.20 point 4.40 negative point to 1.4 negative one negative 1.2. Yeah.

Okay for this one. We have a is equal to 12 negative. One 011 and zero. Negative 11 So the characteristic equation for this problem is given by negative Lambda Cubed plus three Lambda squared minus four. Lambda plus two is equal to zero. And when we solve this equation, it's a cubic equation. So you will get the three argon values as 11 plus I and one minus. I noticed that these talking visor complex congregants. So now if we have the Lambda equals one, then upon solving the system, eh? Minus I times u equals zero. We will get that use equal t times 100 and for Lambda equals one. Plus I, using a similar process, we end up getting that you sequel to a T times I'm minus two negative I and one no, for Lambda Contra Kit equals one minus I, which is given here. Then that implies that you is equal to it. Turns out that the Egan vectors are also conflicts congregates of each other. So you was simply gonna be equal to a T times negative. I'm minus two guy and one

We're given this magic A We're universe first. Me from the convertible meeting room. Without it, the determinant they You could have zero in a but not in veritable works. Check it. A convertible. What do you say? Actually, I read it down here. Let's find a determining a check of the convertible or not. 111 First, I'm gonna high road to buy world one by negative one and had it wrote to So I guess one might one minus one zero. Making one plus 21 No one here. Next I'm gonna multiply growth three by negative one times wrote to I get 111 negative. Q one is negative one. You know, the determining the mortification old the numbers in the pivot in the diagonal interment is clearly not so. Therefore, we can find a neighbor nullifying chambers through the over inside the right chambers on this side. Very eight in the side. You're a here you have the identity matrix for three by three One here is you here alone? Now we're gonna really do until this side here. It looks like this. Once we do that, we will get a members on this side Look for reduced. Well, we already thought before we're finding the determinant. Do it again. First they can about this here. 11 now weaken Can't hold this position here. Negative one. They won negative times. Negative. 101 Negative. 101 Here one. Now weaken. We can scale the throw here. We can divide the group by negative one. We get negative here. Also here. Positive here. Now I can scale road three by minus a few. Added row to cancel this The negative too. Times road Here. That positive you minus one. That's one. Make a few plus one minus one. Two zeros too. You get one Next. We just need get rid of this. We can. He gave the period. Rowing added to the first would be a bit of this one. Here. You never get here from zero and in one one to negative one plus 01 and 101 Now you get a second road out of the first road in negative. One plus two. Just one. You have one plus minus +10 You have minus to plus one. You hear? This is the identity matrix implies on this side. He had a members say in verse, should be one bureau minus one one, minus 12 and minus 11 minus 11

I would probably want to discuss why the determinant of the matrix, given My 1 -12, 1 to 19 of one, 1 -1, 2 Is equal to zero. Now one important property of determinants is that if you have a row repeated, then that determinant is zero. Now notice here that row one is repeated in row three, so row one is equal to row three, so for that reason because we have a row repeated, We can say that the determinant is zero. Yeah.


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