Show that the eigenvalues for the (m 1) by (m 1) tridiagonal method matrix A given by are with corresponding eigenvectors v(i), where v(i)j =

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

are

with corresponding eigenvectors v(i), where v(i)j = sin(ijπ/m).

jsi-lorj = 1+1, 1-21, j-i, 0, oterwise asl--(sin ): for each i-12 m-1.