Question 1: Consider the matrix 64 48 600 1 84 112 0 A = 7 48 36 800 288 384 0 and the vector (3 = [2, 10, 11,3, 55F. (a) Find the singular value decomposition of A. In other words, nd orthogonal matrices U and V such that A = UEVT where E has the form 01 0 0 0 0'2 0 E = 0 0 0'3 0 0 0 0 0 0 and 01 2 02 Z 03 Z 0. You may use the computer for arithmetic calculations (such as nding ATA) and for nding the eigenvalues and corresponding eigenspaces of ATA, but otherwise do these calculations by hand. The point here is for you to work through an example in order to understand how the singular value decomposition is found. (b) Find the pseudoinverse of A, AT. (0) Use the pseudoinverse to nd the solution to the least squares problem minmeka ||b Axll- (d) Find proj{Col A}b. Write your answer as a linear combination of the columns of U. Use your answer to nd the solution to the least squares problem in part (c) as a linear combination of the columns of V and notice it is the same answer as you obtained in part (c)