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...

help?