Question: Let A be an m x n matrix, let P be the projection matrix that projects vectors in Rm onto R(A), and let Q be

Let A be an m x n matrix, let P be the projection matrix that projects vectors in Rm onto R(A), and let Q be the projection matrix that projects vectors in R" onto R(AT). Show that
(a) I - P is the projection matrix from Rm onto N(AT).
(b) I - Q is the projection matrix from Rm onto N(A).

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