A is a 3 x 3 matrix with eigenvectors v1 = [1 0 0], v2 = [1 1 0], v3 = [1 1 1] (all vertical) corresponding to eigenvalues x1 = -1/3, x2 = 1/3, x3 = 1, respectively and x = [2 1 2].

Find (A^k)x. What happens as k approaches infinity?

I don't even know where to begin on this one.

Thanks for the help!