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The matrix is A:

(1 0 0 0

1 0 0 1

0 1 0 0

0 0 1 0)

I got the eigen values as:

λ

_{1}= 1, λ

_{2}= λ

_{3}= λ

_{4}= 0

For λ

_{1}:

The eigen vector V

_{1}is (0, 1, 1, 1).

For λ

_{2}-> λ

_{4}:

The only eigen vector I could make out is: V

_{2}(0, 0, 0, 0).

To calculate the remaining eigen vectors I solved for P using the formula (A-λI)P = K

Where K is an eigenvector of the matrix A associated with the eigenvalue (In this case V

_{2}). But substituting λ

_{2}and V

_{2}into the equation will only lead back again to the same equation which I don't think is correct. Is there a better method I can follow or is there something I am not doing correctly?

Thanks