Consider the matrix 1 M = C -3 4 1 where c is a real number. (a) If M is the augmented matrix of a system of linear equations, determine the number of equations and the number of variable. Justify your answer. (b) If M is the augmented matrix of a system of linear equations, find the value(s) of c such that the system is consistent. Justify your answer. 5 (c) If the matrix 1 C 2 0 -3 4 1 0 is the augmentation matrix of a homogeneous system of linear equations, determine the number of equations and the number of variables. Justify your answer.