Problem 5. (Optional) Verify that A1-2 cos (m+1)' j = 1,..., m. V = sin j 2j , sin m+1 m+1 mj sin m+ are eigenvalues and eigenvectors of the matrix T = Id-Id_-Id+. In other words, show that (A; IdT)v; = 0. Problem 6. Let \; be defined as in the previous problem. Suppose that -1