Let

Your solution is

So you must compute But how? It turns out that with this particular you can easily compute the th power, thus enabling you to compute

Normally, you'd use the eigenvalue expansion. But, as you've noticed, you can't do that with this matrix. You could try to use generalized eigenvectors. Another approach is to try to compute the nth power directly, which I think you can do here. What do you get when you compute the nth power of A?