4. (25 points) True/False. Briefly explain or you can give a counterexample if false. (a) Every invertible matrix A has a PLU factorization, i.e., PA = LU. (b) The set of all solutions of r - y-22=0 is a subspace of R. (c) The column space of an m by n matrix is a subspace of Rn. (d) If A is invertible, then N(A) = 0. (e) If b is in C(A), then Az = b has a solution.