Hello, I need the answer to this question please.

3 (56 pts) Consider the following system of equations: ac + y + 4z - 2 2xty + a-z - 2 - 32 = a where a is a parameter. (a) Write the system as a (3 x 3) matrix system AX = d where X Find the determinant of the coefficient matrix A. For what values of a does the system have one, none or infinitely many solutions? Justify your answers. (21 pts) (b) Assuming that the system has one unique solution, use matrix inversion to find the solution. (18 pts) (c) Assuming that the system has one unique solution, use Cramer's rule to find c. (10 points) (d) Replace the right-hand sides of the system by zeros. What condition(s) should you impose on the parameter a such that the system does not have the trivial solution? Justify your answer. (7 points)