1. The problem statement, all variables and given/known data 1.Prove that if A is a real matrix then At A is diagonalisable. 2. Given a known 3*3 matrix A, Calculate the maximum and minimum values of ||Ax|| on the sphere ||x|| = 1. 2. Relevant equations 3. The attempt at a solution For the first problem, I'm thinking of proving that AtA is symmetric, but I'm not sure which properties to use. For the second one, is X a 3*n matrix? Do I need to discuss n? Any help is greatly appreciated!