Question: Question 5 numerical methods Problem 5. (Optional) Verify that dj :=1 - 2 cos (m + 1) j = 1, ...,m. vj = sin min

Question 5 numerical methods

Problem 5. (Optional) Verify that dj :=1 - 2 cos (m + 1) j = 1, ...,m. vj = sin min sin ., sin m +1 m +1 m +1 are eigenvalues and eigenvectors of the matrix T = Id-Id_ -Id. . In other words, show that (), Id-T)vj = 0. Problem 6. Let Aj be defined as in the previous problem. Suppose that -1

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