uggh, sorry, I changed the question slightly so I could try work out the question myself for a different set of vectors. The original question was:

Suppose that for some 3x3 matrix A, we have A(1,0,-1) = (2,0,-2), and A(1,2,0) = (2,4,0).

a) Find one eigenvalue of A.

b) Explain why (0,2,1) is an eigenvector for this eigenvalue and hence find A(0,2,1).