Let A be an m x n matrix. Use the steps below to show that a vector x in Rⁿ satisfies Ax = 0 if and only if A^TAx = 0. This will show that NulA = NulA^TA.
a. Show that if Ax = 0, then A^TAx = 0.
b. Suppose A^TAx = 0. Explain why x^TA^TAx = 0, and use this to show that Ax = 0.