2x + 4z = −2

−x + 2y − 3z = 4

x + 2y + z = k

Row-reduce the augmented matrix for the given system and then answer each of the following questions.

(a) For what value(s) ofk does the system of linear equations have a unique solution?

(b) For what value(s) of k does the system of linear equations have no solution?

(c) For what value(s) of k does the system of linear equations have infinitely many solutions?

(d) For k where the system has infinitely many solutions, solve the system.