The given system of equations is

x + y + z = 2

3x – y + 2z = 6

3x + y + z = -18

The matrix equation corresponding to this system is :-

Let A =

|A| = = 1(-1-2) -1(3-6) + 1(3+3)

= -3+3+6 = 6

i.e., |A| 0

A unique solution of the system exists.