Prove Theorem 6:
a. Suppose p is a solution of Ax = b, so that Ap = b. Let vh be any solution of the homogeneous equation Ax = 0, and let w = p C vh. Show that w is a solution of Ax = b.
b. Let w be any solution of Ax = b, and define vh = w - p. Show that vh is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh, with p a particular solution of Ax = b and vh a solution of Ax = 0.