- --. Assume an m x n matrix A of rank n (and m > n) and let the reduced SVD of A = UCV with U being m x n, E being n x n and V being n X n. . (5 points) Write P = A(ATA)-'AT in terms of the reduced singular value decomposition matrix U. . (5 points) Interpret your result taking care to explain the relationship between your expression for P and the rank of the matrix. . (15 points) Then rewrite the least-squares orthogonality principle for the problem minx ||b - Axl|? in the form Cx = Db where C and D are written in terms of the SVD of A. C should not contain U and D should not contain V. Show all steps and interpret your result in terms of the two vector spaces R" and R"