1. The problem statement, all variables and given/known data Compute [1 1]^n [ 1] This is what my book has. I am assuming the blank means 0 (please tell me if this is not the case). 2. Relevant equations None really (matrix multiplication) 3. The attempt at a solution I did n = 1, 2, 3, 4 and found a patten. It looks like: [1 1]^n [ 1] = [1 n] [ 1] But how do I show that? Obviously showing it for a couple cases doesn't mean it's actually true. Inductively, I can show the n = 2 case is true. but I don't really know how to show the n+1 case is true other than write [1 1]^n+1 [ 1] = [1 n+1] [ 1] but that seems a little unsatisfactory or like I'm skipping steps or something. How do you do it?