Consider the following linear system with a and b unknown non-zero constants.

x1 − 3x2 + x3 = 4

2x1 − 8x3 = −2

−6x1 + 6x2 + ax3 = second

(a) For what values of a and b does the system have infinitely many solutions?

(b) Given an example of a and b where the system has exactly one solution.

(c) Give an example of a and b for which the system has no solution