You should get a row of zeroes. For every eigenvalue there are infinitely-many associated eigenvectors.
For example, the eigenvectors associated with are vectors of the form
Find all the other eigenvalues and eigenvectors.
I have found the eigenvalues for this matrix being , &
I have subtracted your eigenvalues from the diagonal to get the following matricies
My problem is that I am stuck on where to go from here. I have used the elimination method but I always end up with a row of zeros and am unsure on where to go from there.
Any help would be appreciated.