Question: Let Pk and Uk be defined as in Exercise 9. Show that (a) Pk+1Uk+1 = PkAk+1Uk = APkUk (b) PkUk = Ak and hence (Q1Q2

Let Pk and Uk be defined as in Exercise 9. Show that
(a) Pk+1Uk+1 = PkAk+1Uk = APkUk
(b) PkUk = Ak and hence
(Q1Q2 . . . Qk)(Rk . . .R2R1)
is the QR factorization of Ak.

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