Let A be an m x n matrix of rank n and let be Rm. If Q

Question:

Let A be an m x n matrix of rank n and let be Rm. If Q and R are the matrices derived from applying the Gram-Schmidt process to the column vectors of A and
p = c1q1 + c2q2 + --- + cnqn
is the projection of b onto R(A), then show that:
(a) c = QTb
(b) p= QQTb
(c) QQT = A{ATA)-1 AT