I have found that the eigenvalues are and
However finding the eigenvectors is where I get a little confused. Looking first at the value we get:
So for the eigenvector do I just choose any values for e2 and e3. For instance would the vector: work?
Further since this is a repeated roots case don't I need to find another matrix such that:
However, trying to solve this I get the equation:
which I think has no solutions...