Consider the system of equations X + y - Z = a X Y + 2z = b 3x + y C (a) Find the general solution of the homogeneous equation. (b) For a = 1, b = 2, c = 4, a particular solution of the non- homogeneous system of equations is x = 1, y = 1, z= 1. Write the general solution for this non-homogeneous system of equa- tions. (c) Find a condition on a, b and c which must be satisfied in order for the system to be consistent. (d) Give one example of a case where the system is not consis- tent.