Show that the eigenvalues for the (m 1) by (m 1) tridiagonal method matrix A given by

Chapter 12, Problem 15

(choose chapter or problem)

Show that the eigenvalues for the (m 1) by (m 1) tridiagonal method matrix A given by , y 1 or y / + I, 1 2A,, y i, 0, otherwise are / in \ 2 /r, = 1 4A I sin , for each i = 1,2 m 1, V 2;n / with corresponding eigenvectors v 1 ' 1 , where uj" = sin '-jA

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