Problem 2 An application of diagonalization is the computation of matrix powers. In Homework 8, you 6 diagonalized the matrix A = 2 7 , i.e. found S and B such that B is diagonal and SAS = B. 3 One possible choice is S = and B - 8 8] i) Using the fact that A = SBS-1, justify the identity At = SB'S-1 for any positive integer t. ii) State a closed-form expression for Bt, and hence deduce a closed-form expression for At