We consider the LU iteration applied to a symmetric matrix. Assume that Ao E Riki is symmetric and positive-definite. We produce a sequence of matrices A; using the following algorithm: Ai = Gi Gi, Aitl = GiGT, (13) 2 where Gi are upper-triangular matrices. Consider now A', the matrix obtained after one step of the QR iteration, that is, Ao = QR, A' = RQ. (14) We assume that the diagonal of R is positive. (a) [10 bonus pts] Use A to show that R = GIGo (15) (b) [10 bonus pts] Show that A' = A2 (16)