00:01
Hi, here in this question we are given that the matrix a equals to 3222 -202 -4 -2 -3.
00:12
Now here we need to find the eigenvalues and the eigenvectors of the given matrix.
00:18
So here first of all we'll find the value of determinant of a minus lambda i.
00:23
So this can be also written as determinant of 3 minus lambda 2 -2 -2 -2 -2.
00:30
0 minus lambda 2, 4, 2 and again 3 minus lambda.
00:36
Now here on solving this determinant we have value equals to minus lambda cube plus 6 lambda square plus 7 lambda.
00:47
So here on simplifying further we have minus lambda multiplied with lambda plus 1 multiplied with lambda minus 7.
00:54
So here taking characteristic equation equals to 0.
00:58
So here on simplifying this we have eigenvalue as lambda 1 equals to 0, lambda 2 equals to minus 1 and lambda 3 equals to 7.
01:10
So here these are our required eigenvalues.
01:13
Now using the eigen values we need to find the eigenvectors.
01:17
So here for lambda 1 equals to 0 we need to find the eigenvector v1.
01:21
Now here we know that in order to find the eigenvector we need to find the value of a minus...