We know from the SVD Theorem 4.1.1 in [1] that any nonzero A e Rnxm with rank r can be expressed as the product (called the Singular Value Decomposition of A): A = USVT. (1.1) where U e R"x", V e Rxi are orthogonal, and Ee R"x", with 01 02 = OT 01 >02>...>0, > 0. (1.2) 0 Show that the SVD implies both of the following equations: AV = U, ATU = V. We know from the SVD Theorem 4.1.1 in [1] that any nonzero A e Rnxm with rank r can be expressed as the product (called the Singular Value Decomposition of A): A = USVT. (1.1) where U e R"x", V e Rxi are orthogonal, and Ee R"x", with 01 02 = OT 01 >02>...>0, > 0. (1.2) 0 Show that the SVD implies both of the following equations: AV = U, ATU = V