1. The problem statement, all variables and given/known data Suppose that the 2x2 matrix A has eigenvalues lambda = 1,3 with corresponding eigenvectors [2,-1]^T and [3,2]^T. Find a formula for the entries of A^n for any integer n. And then, find A and A^-1 from your formula. 2. Relevant equations Ax = lambda X (P^-1)AP = D A = PDP^-1 3. The attempt at a solution I've been trying to figure this out for a long time. I'm really not sure where to start... If anyone could provide some sort of guidance on how to begin this problem... that would be really helpful. I've tried using the above formulas, but I'm just not sure how to get a generalized formula. I could find A and A^-1 individually without the generalized formula, but the problem asks for it; thanks in advance for even the slightest hint.