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5 . [-/1 Points]DETAILSLARLINALG8 2.3.053.Find x such that the matrix is equal to its own inverse:XA =-4 ~7X =...

Question

5 . [-/1 Points]DETAILSLARLINALG8 2.3.053.Find x such that the matrix is equal to its own inverse:XA =-4 ~7X =

5 . [-/1 Points] DETAILS LARLINALG8 2.3.053. Find x such that the matrix is equal to its own inverse: X A = -4 ~7 X =



Answers

Find the inverse of the matrix. For what value(s) of $x$, if any, does the matrix have no inverse?
$\left[\begin{array}{cc}{x} & {1} \\ {-x} & {\frac{1}{x-1}}\end{array}\right]$

This problem involves the idea of finding the inverse of a given matrix. We are going to use a method that will involve row operations and the identity matrix. So I'm going to start off this problem by taking the given matrix, writing it down, you draw a vertical power. And since it's given matrix is a two by two matrix, I'm gonna ride the identity matrix four. A two x 2 on the right hand side of the vertical boy. Now, the goal in a problem like this, he's in the row operations. Here's the goal that I'm going to go forward. My row operations. I want to transform that green matrix that I just wrote to where the identity matrix is now on the left hand side of the vertical bar and then the right hand side is going to be the inverse for the given matrix. So again, our row operations were going to transform the left hand side into this identity matrix. Okay, so let's get started with this problem. What I'm gonna do first of all, So I'm going to make a new role warned by taking roti most planet by negative wand and admit to row one. So let's do that. I'm gonna leave road to what it is right now. Yeah. And I'm gonna take road two times a negative one and add that two row on. Okay, so it's negative one added to two is 1 that Fox native one added to one is C. Webb. Yeah, zero added to one is 1 And the -1 and zero is negative war. Okay. So I've made that change can. Now what I need to do is I need to make this number of zero without losing other things I have here. So what I'm going to do now is I'm going to get a new road to by taking my current role on Terms of -1 And they ended two road to so I'm gonna take this times a negative one and added to road to All right. So I'm gonna keep rolling what it is and I will do my row operation Because it's a negative one at 20 zero. I had a torn is one -1 added to zero is -1. When I multiply here, that's a positive one added to one is too. So I have made the transformation that I said I needed to make that my goal was you know, here's my identity matrix I needed and then I said this side would end up being the inverse. So the inverse of the given matrix. Yeah, the inverse of given matrixes. The two x 2 matrix of 1 -1 negative 12 two. Thank you.

For calculating the inverse off these batteries too. Minus three. Four, Hank. Well, fish work on it, much less a the inverse off the monstrous because one divided by the terminal, which is eight minus four minus three is 12. So if that comes Yes. Clark Defense line four, minus three. On Here it is. Four minus four on. Yeah, Plus. So it becomes one divided by five. Yeah. Three divided by 20 minus one. Well, I just like five and one dividers waiting.

Hello. So are given matrix is the matrix 15? Negative one? Negative four. So you write that matrix down and we put this line and put the two by two identity matrix on the right now. We want to perform elementary row operations to then convert the identity matrix here to the left hand side. And what we have on the right hand side is going to then be our inverse matrix. So what we can do here is well let's just do um let's first we have a one already right? We can just do um basically add row one too low to to get a zero beneath. And then um we can take negative five times row to add that to roll one. And then we're going to get the identity on the left. So we get one 001. And then on the right hand side of this bar we get negative for -511. So therefore what we have now on the right hand side of the bar here is going to be is going to be um our inverse matrix. So therefore we have that the inverse here, a inverse Is going to be equal to negative 4 -5 11

This question be her air metrics moves in us. We need to find out the X one. We're in a fix who you get one by experience from this murderous ah can be compared with the metrics a the city now in order to find all the metrics in worse here. So we had a formula a the Manus BC marquee player with the minus B, then a c A and 80 minutes BC's Norby called zero This is a total one day X by ex Manus one Let's pigs, then we have d one by X minus one. Here we have X city minus one. Here we have X and we have knicks. So the inverse about you will be X minus one upon excess square and we have one of born X minus one minus one x x. So this is the inverse of this matrix on. If we have to check, the weather is off X for which a nose does not exist in a D minus. B C is equal there. Zero. So we need. If I know the Wailers affects for that, this implies X minus one by city. You will be. It's a square employees X minus one Civically Tzeitel. It's skin meter denies pictures square minus one. This woman by There's implements X sick quartile this eagle.


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