Let A Rmxn with m > n and A = [10uv be a singular value decomposition of A. Assume that > ... > 0. 1. (7 points) Consider A = 1(1/0) viu. Prove that for any y Rm, AAy is the projection of y to the subspace span (u,..., un) CRm. (You can use the definition in page 5, Lecture 19.) 2. (7 points) Additionally given b = Rm, we want to find R" such that || Ax b|| is minimized. (Recall that ||v||2 Ei vis its Euclidean length.) Prove that x = Ab is an optimal solution. (Hint: Geometrically, given A and b, what should Ar be in order to minimize || Axb||?) =