Find the eigenvalues of A. < b m a t r i x

Find the eigenvalues of A. $\begin{bmatrix} 9 & 0 & 1 \ 2 & 3 & 2 \ 1 & 0 & 9 \end{bmatrix}$ Enter the eigenvalues below. Enter eigenvalues from smallest to largest. If eigenvalues are a multiple zero of the characteristic equation then enter them repeatedly. e.g. -1,2,2 or -3,-3,1.

Transcript

00:01 Let's have a look at the question.

00:02 So the question state that find the eigenvalues, find an eigenvector corresponding to each eigenvalue, do this first by hand and then use whatever technology you have available to check your results.

00:16 Remember that any constant multiple of the eigenvector you will find will also be an eigenvector.

00:22 And order eigenvalues from the smallest to largest real part then by imaginary part.

00:28 So we have that d is equals to 1, 3, minus 3 and minus 5.

00:36 So here we will start from forming a new matrix by subtracting lambda from the diagonal entries of the given matrix.

00:46 So we can write this as 1 minus lambda minus 3 then 3 and minus lambda minus 5.

00:57 So here let us find the determinant of the obtained matrix so that will be equals to 1 minus lambda multiplied with here we have minus lambda minus 5 and then subtracted with minus 3 multiplied with 3.

01:21 So on solving here we will get this as minus lambda multiplied with 1 then we have plus 1 multiplied with minus 5 then we will have minus lambda multiplied with minus lambda and then we will have minus lambda multiplied with minus 5, then minus, minus 3 multiplied with 3 is minus 9.

01:47 So here we will get minus lambda minus 5 then plus lambda square then plus 5 lambda and plus 9.

02:00 So on solving this we will get this as lambda square then we will have plus 4 lambda and plus 4.

02:10 So this can be written as lambda square plus 2 lambda plus 2 lambda plus 4.

02:17 So here taking lambda common we have lambda plus 2 and plus taking 2 common we have lambda plus 2.

02:25 So we get lambda plus 2 multiplied with lambda plus 2...

Question

Find the eigenvalues of A. $\begin{bmatrix} 9 & 0 & 1 \ 2 & 3 & 2 \ 1 & 0 & 9 \end{bmatrix}$ Enter the eigenvalues below. Enter eigenvalues from smallest to largest. If eigenvalues are a multiple zero of the characteristic equation then enter them repeatedly. e.g. -1,2,2 or -3,-3,1.

Please give Ace some feedback