Suppose that the augmented matrix of a system Ac = b is transformed into a matrix (A'B') in reduced row echelon form by a finite sequence of elementary row operations. (a) Prove that rank(A) + rank(A'B') if and only if (A'B') contains a row in which the only nonzero entry lies in the last column. (b) Deduce that Ax = b is consistent if and only if (A'|b') contains no row in which the only nonzero entry lies in the last column.