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3e" 42* - (1 poini) Lei 4 = 2ede 32"a) Fina ine deieminant oi A_ det( A)() Find ihe mjuix 0i coiz ciors Of(C) Flna tne acjpint 01 Aedi( A) =(d) Find ite I...

Question

3e" 42* - (1 poini) Lei 4 = 2ede 32"a) Fina ine deieminant oi A_ det( A)() Find ihe mjuix 0i coiz ciors Of(C) Flna tne acjpint 01 Aedi( A) =(d) Find ite Inverse oi A.

3e" 42* - (1 poini) Lei 4 = 2ede 32" a) Fina ine deieminant oi A_ det( A) () Find ihe mjuix 0i coiz ciors Of (C) Flna tne acjpint 01 A edi( A) = (d) Find ite Inverse oi A.



Answers

Work each problem. Let $A=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & -1\end{array}\right] .$ Show that $A^{3}=I_{3},$ and use this result to find the inverse of $A$.

The region FX, which is 1/4 2 x minus three. So difficulty near funds on the graph of this mountain. Well, look, something like this. This is the X axis and this is the Y axis. When we will take extra thick Puerto Rico, we will get why they call two minus three. So, Geno, common ministry similarly will get why is equal to zero. We will get exited. Acquittal three by two. So this is three by two comma Jiro. So the graph off this equation will look something like this. This is the graph of difference on FX is equal to x ministry, which is just straight line. Now the question is, if the consummate 11 or not, so we can see for each and every value off X there is a unique value of why Then we can share their this once on the job 11 funds Similarly, if it is 11 we have to find the formula for downwards. So to find then worse wisely. Quarter two x ministry We will interchange x and y so we will get X is equal. Toto, Why ministry? Now we will find a wife from here, so X plus three is 1/4. So I Therefore, why is the quarto X plus three by Don't So this is F in Watts expletives Acquittal X plus three by toe.

Christian were given the metrics. A were asked to show that a Q is the identity matrix I and were asked to use this to find the inverse poppy. So these were the two things for us to do. So let's go ahead and do that. So a Cube is basically eight times eight times a so let's do eight times three times. So we have 100 00 minus one throw one minus one 00 minus 101 minus one times. Yeah, so let's calculate the product of these two matrices first and then to the next one. So here for Matrix products, we're basically going to take first rule times. So first column. So we have one, and then we take the first row and the second column. So we have zero zero and 00 We take first through third column, 0000 Now, for our second rule, we take the second row. So we have second role. First column. So we have 00 zero, which is basically zero second row second column. We have 00 minus one and then second row. Third column. We have 00 and one. That's one. Here. Yeah, for our third. So we take third row times. First column. So we have 000 Basically zero third row times, Second column. We have 00 and once Girls. Girl minus one. And then for the last item, we have zero minus one last one. So that gives us zero. So it a cube is equals to pay times eight times eight. So we have this times egg. So we basically have a squared Times eight and we have calculated he squared over here. So to calculate the square times p, we have 100 zero minus 110 minus 10 times a, which is 100 00 minus one and 01 minus one. So with that, we get So we take our first raw first column. We had one first rule Second column. We get zero first draw. Third column. We have zero second role. Yeah, First column. You get to, uh, second rule. Second column ahead One second Rule third call. We get zero. Yeah, plus one minus one, which is zero third rules. First column. Yes. Europe third row, second column. We get 000 again. Third row, third column. We get zero plus one so they get one which is basically equals two. The identity matrix 53 So we basically shown that therefore, if you because stupid find three. So the first part of the question is solved now in the second part, whereas to use this result to find the inverse off A. So so we know that a times K universe equals to the identity matrix. And we also know that a Q basically calls to the identity matrix so he times he squared is equals to the identity matrix. And from association here, we know that a inverse is actually equal to K squared, which we have already found in our first part here. So we took eight times the times, which was basically a square times s. So we actually found that universe, which is he squared? Is this matrix right here which is 100 zero minus 11 and zero minus 10 And so we found that we used this result to find the inverse off big, which is right here

In the kitchen given medics are that is first metrics metrics safe with the element give anus that is 57 Okay. Do three and metrics be given in the collusion with the elements. That is 317 managed to And five. Now when the question it is asking to show that be in myself. Medics A. So we have to prove it. It means so. No. I will use the property that it be the inverse of A. Then the property is tradition. Yeah. Product in was will you unit metrics of same order which have my T. V. A. Yeah. So it means it be easy in more Sophie then A B will do unit medics. So this is a man property by which we have to get a result of unit metrics. It means it be in words of faith. So what I will do is I will try to metrics of a metrics and metrics be then I'm taking a multiplication of A. And B. So it will be witness. Yeah. Medics say is 57 23 And metrics we status three minus seven managed to and five No for taking a multiplication of A and B. We have to use A dot product. So in the door products we are taking a multiplication of first. When first column. For first element means for this place then for this place we are doing a fast bro Multiplication with 2nd row. So the second column then for this place we are for this place. What we do is second role multiplied with the first column. And for this second role with second column all multiplied with their matching members. Means I will try to explain by multiplying in written form. So it will be multiply this for this position The value is 35. five times of three plus seven times of five. And for this position the value is five times of -7 plus fight less seven times or five. No. And for this position value is studies two times of three plus three times of minus two. And for this position value is two times of -7 Plus three times of five. No. So all this then I will get the metrics that is After falling. I will get one judo 01. As you see this is a unit metrics. So in the result I had to find I had got the you meet metrics. So I can say that is re that'd be easy in worse off metrics. A means matrix B. So Oh so it means we have brought it. So hand side for execution. Thank you.

In the kitchen given medics are that is first metrics metrics safe with the element give anus that is 57 Okay. Do three and metrics be given institution with the elements that is 317 managed to and five. Now when the question it is asking to show that be in myself. Matic A. So we are to prove it. It means so No. I will use the property that it be the inverse of A. Then the property is tradition. Yeah. Product in was will you unit metrics of same order which help Mattie Fae. Yeah. So it means it be easy in more Sophie then A B will do unit medics. So this is a man property by which we have to get a result of unit metrics. It means it be in matters of faith. So what I will do is I will try to metrics of a metrics and metrics be then I'm taking a multiplication of A and B. So it will be written us. Yeah. Medics say is 57 23 And metrics we studies three minus seven. Managed to and five No for taking a multiplication of A and B. We have to use A dot product. So in the door products we are taking a multiplication of first. When First column for 1st element means for this place then for this place we are doing a fast bro Multiplication with 2nd row. So the second column then for this place we are for this place. What we do is second role multiplied with the first column. And for this second roll the second column all are multiplied with their matching members. Means I will try to explain by multiplying in written form. So it will be multiply this for this position The value is that is five, five times of three plus seven times of five. And for this position the value is five times of -7 plus fight less seven times or five. No. And for this position value is studies two times of three plus three times of minus two. And for this position value is two times of -7 Plus three times of five. No. So all this, then I will get the metrics that is After falling. I will get one judo 01. As you see this is a unit metrics. So in the result I had to find I had got the you meet metrics. So I can say that is re that'd be easy in myself metrics A means matrix B. So Oh so it means we have brought it so hence I had followed occasion. Thank you.


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