Question: Let A be an n x n real matrix with the property that AT = A, let x be any vector in Cn, and let

Let A be an n x n real matrix with the property that AT = A, let x be any vector in Cn, and let q = xrAx. The equalities below show that q is a real number by verifying that q = q. Give a reason for each step.

7-' Ax = x' Ax = x'AX = (x" AX) = x Ax= q %3D %3D (c) (b) (e) (a) (d)

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