4. Let 2 1 1 A = 121 1 1 2 (a) (2 marks) Find all eigenvalues of A. (b) (5 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace). (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D = P-1AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1. (e) (2 marks) Use your answers from part (a) to (d) to write down a matrix product (not involving powers of matrices) equal to Am, where m is a pos- itive integer. Note that you do not actually have to multiply the matrices together (although you're certainly welcome to if you'd like)