Eigenvectors

(in case my ascii treatment isn't obvious, M is a matrix)

M = (k 3)
____(0 2) , where k is not equal to 2.

By finding and solving the characteristic equation, I've found the eigenvalues to be k and 2. However, the problem comes in when I try to find a corresponding eigenvector to the eigenvalue k.

I get:

ka + 3b = ka
2b = kb

So I think b has to equal 0, but how do I find the possible values of k?

Oh by the way, for 2 by 2 matrices, there is only 1 equation and two variables (for 3 by 3, there are 2 eqns are 3 variables and so on). The two equations you got are actually the same.