Question: 1. Let A be a singular upper Hessenberg (non-symmetric) matrix having no zeroentries on its subdiagonal. Show that the unshifted QR algorithm applied to A

1. Let A be a singular upper Hessenberg (non-symmetric) matrix having no zeroentries on its subdiagonal. Show that the unshifted QR algorithm applied to A produces anexact eigenvalue after only one iteration.

2.Let A be a symmetric tridiagonal matrix. Show that the shifted QR algorithmpreserves the tridiagonal structure in A^(k). (If you wish, you can prove this for a 4x4 matrix.)

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