00:01
I here for the given question, we are given matrix a is equal to 7 2 8 0 minus 3 0 minus 10 minus 2 and minus 11.
00:12
Now here for the given matrix a it can be written as p multiplied with diagonal matrix multiplied with p inverse using this we need to find what is the value of matrix p and what is the value of its diagonal matrix.
00:24
So here we need to calculate the value of eigenvalues and eigenvectors.
00:27
So here determinant of a minus lambda i can be written as equal to 0.
00:31
So here in our case, we have 7 minus lambda 2 8 0 minus 3 minus lambda 0 minus 10 minus 2 minus 11 minus lambda.
00:41
So here this is equal to 0 now solving this given determinant here.
00:45
We have lambda q minus lambda q minus 7 lambda square minus 5 15 lambda is equal to 0.
00:52
So solving this we have minus lambda plus 1 multiplied with lambda square plus 6 lambda plus 9 is equal to 0 here.
01:00
This can be again written as minus lambda plus 1 multiplied with lambda plus 3 whole square is equal to 0.
01:07
So eigenvalue lambda equals to 1 and lambda equals to minus 3 and minus 3.
01:14
So here these are the three eigenvalues.
01:17
Now, we need to calculate the corresponding eigenvectors...