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0 Khnen telofalte 0eattnmeno F 1...

Question

0 Khnen telofalte 0eattnmeno F 1

0 Khnen telofalte 0 eattnmeno F 1



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

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.

In this motion we have to use the reduction to find the universes of the given mattresses if they exist. And check it by multiplication. Let us consider the metrics deal one 10. And on the right side identity metrics or for that too 10 01. Now we will roll reduce the parliamentary. They will interchange. Okay. 1st and 2nd role our metrics becomes talk 10 01. And on the right side. Do you know? one 10. So we can write a universe equals two 0110. Now we will check it by multiplication. We will multiply a matrix by invest matrix. So we can write 0110 multiplied by 01 10. Now we will do the multiplication. Mhm zero times 0. We will first multiply first row with first column zero times zero plus one times one. Now we will multiply first love this second column. There are times one Plus one times 0. Similarly, we can write one times zero. The first few times one one times one Plus zero times 0 own simply find it began to metrics 1001. So we can t inverse matrix Sequels to identity matrix. Mhm. Thank you

In this question we have to use row reduction to find the invoices of the given mattresses if they exist. And check it by multiplication. Now let us consider It takes 111 011100. And on the right side identity metrics of all three. 100 010 001. Now they will pro radio steam metrics. We will apply the operation three store store Our 3 -11 and Arvin starts to Urban -R2. On applying these operations we got the metrics 100 011 0 -1 -1. And on the right side 1 -10 Vettel one vehicle -1 Little one. Now again we will apply the operation Our three stores too. I want to yeah on applying this operation regard the metrics one beetles, beetle, 011 000. And on the right side 1 -10. Mhm 01 zero -111. Mhm. Since we observe that left hand side of the metrics is not an identity matrix. Therefore inverse of matrix. There does not exist exist. Hence a singular romantic. Yeah. Okay. Thank you.

In this ocean of metrics is given to us. We have to compute the determinant of even metrics. If the determinant is non zero, we have to use the formula for inverting or two by two matrix to can create the inverse of the given metrics. First we'll find the predominant determinant of a matrix equal school one times 1 zero times 0. Don't seem to find it. We get one as a determinant since the determinant of is not equal to zero. Therefore, in both of these metrics exist which can be calculated as metrics A B c E. It was it was 21 divided by early minus busy. Multiplied by metrics B minus b minus key. Mm. Therefore They can obtain was equals two. one divided by determinant of Multiplied by Matrix one deal 01. We have already calculated determinant of a one divided by one, multiplied by 1001 on multiplication. We get the inverse which is yeah. 10. The little one. Mhm. Thank you.


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