Let A be an m n matrix of rank n and let P = A(AT A) 1AT . (a) Show that Pb = b for
Chapter 5, Problem 9(choose chapter or problem)
Let A be an m n matrix of rank n and let P = A(AT A) 1AT . (a) Show that Pb = b for every b R(A). Explain this property in terms of projections. (b) If b R(A) , show that Pb = 0. (c) Give a geometric illustration of parts (a) and (b) if R(A) is a plane through the origin in R3.
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