Please answer all parts.

160 40 40 28: If A = then AT A = 40 100 -80 40 80 100 (a) Use the previous answer to find a reduced singular value decomposition A = U. DV. for A. (b) Find a singular value decomposition A = UCV for A. To make determining U easier recall that (1, 1, 1, 1), (1, 1, -1, -1), (1, -1, -1, 1), (1, -1, 1, -1) is an orthogonal basis for R. (c) Write A as a linear combination of rank 1 matrices