Consider an n x k matrix X with full column rank. Let P = X(X'X)-X' be the usual projection matrix, and let M = 1 - Px. (a) Prove that for any z that is orthogonal to all columns of X, it follows that Pz = 0. (b) Let y = X be a linear combination of the columns of X (B is a k x 1 vector). Prove that My = 0.