Exercise 6.4.3. Suppose that A E M(n,n), B E M(m,n), and C E M(m,m), and define A D X : . Prove that X is invertible if and only if both A and B are. Exercise 6.3.2. Given a vector y E R", define the linear transformation fy : R" -> IR by fy(x) = (x, y), where (., .) is the usual inner product on R" . Compute IIfllop