Problem 10 (10 points). Whenever B can be derived from A by a combination of elementary row and column operations, we write A ~ B, and we say that A and B are equivalent matrices. Since elementary row and column operations are left-hand and right-hand multiplication by elementary matrices, we can say that A ~ B + PAQ = B for nonsingular P and Q. First show if A is m x n such that rank(A) = r, then A ~ Nr = 0 0 0 where Nr is called the rank normal form for A. Using above definition explain why rank( A 0 0 B ) = rank(A) + rank(B)