Let P = A(ATA) 1AT , where A is an mn matrix of rank n. (a) Show that P2 = P. (b) Prove

Chapter 5, Problem 11

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Let P = A(ATA) 1AT , where A is an mn matrix of rank n. (a) Show that P2 = P. (b) Prove that Pk = P for k = 1, 2, . . . . (c) Show that P is symmetric. [Hint: If B is nonsingular, then (B1)T = (BT ) 1.] 1

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