Problem 5. (Optional) Verify that A1-2 cos (m+1)' j = 1,..., m. V = sin j...

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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 <1-0-; <1 for all j = 1,..., m. Show that < 1/2. (That is, D <1/2.) 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 <1-0-; <1 for all j = 1,..., m. Show that < 1/2. (That is, D <1/2.)