1. Suppose Ax = AX and Ay = Oy and A f:. O. Then y is in the nullspace and X is in the
Chapter 6, Problem 18(choose chapter or problem)
1. Suppose Ax = AX and Ay = Oy and A f:. O. Then y is in the nullspace and X is in the column space. They are perpendicular because . Go carefully-why are these subspaces orthogonal? 2. If Ay = {3 y, apply this argument to A - {3!. The eigenvalue of A - {3! moves to zero and the eigenvectors stay the same-so they are perpendicular.
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