Prove the theorems given below

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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.

Reference no: EM131073193

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