Question: PROBLEM 14 Suppose that S is a linear system in x, y, z and w. Assume further that the coefficient of every y that occurs

PROBLEM 14 Suppose that S is a linear system in x, 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' (e) None of these

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