5

0 0 0 0 0 'St H 1 3 Joor...

Question

0 0 0 0 0 'St H 1 3 Joor

0 0 0 0 0 'St H 1 3 Joor



Answers

$\left[ \begin{array}{lll}{1} & {0} & {0} \\ {0} & {0} & {2} \\ {0} & {2} & {0}\end{array}\right]$

In this problem, we have given the mattresses on be an oxidant remind video. The pair of each metrics is the inverse off each other. Let's consider it Mac tricks be find metrics. Be post refined, a productive metrics A and B begin the metrics which is equals toe identity mattress. Now they find a productive be into a The result of markets would be my 00 010 three do which is not equal ist white into Demetris Since the product of too many places on either side are not I'd into demand tricks. The given to my prisons are not in rows on each other.

That's that's one for you with this one. Remember? Our are very so this one doesn't have any solution because we have our last Oh, it was us isn't true. Statement, so we can see that. Is this Listen, but right or all right. What are the right reasons so Or money? Sports. Why you gotta wait a solution? We thought so. This is more only work. Not all right.

So in this problem we're given this matrix which Is a diagonal, right, only has entries on the main diagonal. Everything else is zero and were asked to define the determinant. We can use a matrix calculator to do this with. So what you desmond dot com went to math tools matrix calculator and got this one. So I need a new matrix now and I got five rows and five columns. And the first entry up here Is a -2 And then the entry here is a three And the entry here is a -1 man. She just working my way down the main diagonal here, This is a two And the last entry down here is a -4. There's all my entries now to do the determinant. I go d E t of a and We get -48 for the answer. So there you go. Which by the way, if you multiply the entries on the diagonal there. Look what happens When one is 2 times three is -6. I was in -1 is plus six times two is 12 Times of -4 is -48. Gave us the determinant, didn't it?

Okay, here we have the matrix. That's three by three. And that's given by 011 101110 And we want to find its Eigen values, and I can vectors. So the characteristic equation could be obtained as negative. Lambda cute plus three Lambda plus two is equal to zero. And by solving this you obtain Linda. One common to come on three is equal to negative one in 81 2 Now, for Lambda equals two, we can have the following computation. So we want to solve a minus to I times you is equal to zero and we obtained you is equal to t where tease a free parameter and are that's non zero time stuff Vector 111 Now for Lambda equals negative one we want to solve a plus I times you is equal to zero. So in this case, we obtain the matrix of all ones times you is equal to zero and so you is going to be equal to the following vector So negative s minus t t and s where s and tear free parameters. So let's denote that here s and t our free parameters and are not including the zero value. Then we obtain. This can be written as tee times negative 110 plus s times native one 01 So we have a two dimensional Ivan's face for Ivan value. Lambda equals negative one so that I can vector corresponding to the argon value Lambda equals negative one lives in a two dimensional I'd in space and the even value corresponding to the back of a lambda equals two lives in a one dimensional against peace.


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