The following system of linear equations  2 x+3 y+2 z=9,3 x+2 y+2 z=9, x-y+4 z=8

The given system of equations is 2x+3y+2z=9,3x+2y+2z=9,x-y+4z=8 The determinant of the coefficient matrix is D=2323221-14=210-310+2-5=-20≠0Since the determinant of the coefficient matrix is non zero, the non - homogeneous system of equations has a unique solution.