1. (3+3+4=10 pts.) Every invertible matrix A is the product A = QH of an orthogonal matrix Qand a symmetric matrix H. Assuming that A has a singular value decomposition A = UΣVT, then A = (UVT)(VΣVT). (a) Show that UVT is an orthogonal matrix Q (what is the test for an orthogonal matrix?) (b) Show that VEVT is a symmetric positive definite matrix. (c) What are its eigenvalues and eigenvectors? Why did I need to assume that A is invertible?