PROBLEM 13 Suppose that the augmented matrix of a linear system S is invertible. Then a) S has a unique solution S has infinitely many solutions (c) S is inconsistent d) S may or may not be consistent e) None of these PROBLEM 14 Suppose that S is a linear system in z, y. z and w. Assume further that the coefficient of every y that occurs in S is different from 2. We construct a new system S' from S by changing only the coefficients of y in S according to the following rule: Every coefficient of y in S is first multiplied by -2, and then add 4 to it. Thus, for example. if S has 4 equations and 5.3, 1. -3 are the coefficients of y in the these equations of S. we replace them by -6. -2. 2. 10, respectively. Which of the following is true? a) Both S and S' are consistent or both are inconsistent b) S' may be inconsistent even when S is consistent c) S must be inconsistent if S is inconsistent d) If S is consistent, then so is S' ") None of these