Problem 1 (SVD). Using the singular value decomposition, verify the following facts about the pseudoinverse: a) AAA = A. b) AAA = A. c) If A has full column rank, then At = (ATA)--AT. d) AA is the projection onto R(A). e) The trace of AA is equal to the rank of A (Hint: you might find the Problem 1 (SVD). Using the singular value decomposition, verify the following facts about the pseudoinverse: a) AAA = A. b) AAA = A. c) If A has full column rank, then At = (ATA)--AT. d) AA is the projection onto R(A). e) The trace of AA is equal to the rank of A (Hint: you might find the