Problem 3 (5+10+7+3 = 25 points) To account for variance in measurement errors one considers weighted least squares problems min |W (Ax - b) 1/2, (1) XERn where W is a diagonal matrix with positive diagonal entries (weights) wii > 0. Measurement with small variance have a larger weight wii- This problem applies the SVD to solve the weighted least squares problem (1) with 0 A = (0 1 0 b = -() and W = 1/2 0 0 (a) (5 pts) Diagonalize WA(WA), i.e., find an orthogonal matrix U E R2X2 and a diagonal matrix A E R2x2 such that WA(WA)I = UAUT. (b) (10 pts) Compute the SVD of WA, i.e., find an orthogonal matrix V E R4X4, and a diagonal matrix E E R2x4 such that WA = UEVT. (c) (7 pts) Find all solutions x E R4 of the weighted linear least squares problem. (d) (3 pts) Find the minimum norm solution of the weighted linear least squares