2 1. A system of three equations is defined by kx + 3y –   z = 3 3x –   y +   z = –k –16x – ky – kz = k where k is a positive constant. Given that there is no unique solution to all three equations, (a) show that k = 2 (2) Using k = 2 (b) determine whether the three equations are consistent, justifying your answer. (3) (c) Interpret the answer to part (b) geometrically. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________