In each of the following, find (if possible) conditions on a, b, and c such that the system has no solution, one solution, or infinitely many solutions.
(a) 3x + y - z = a
x - y + 2z = b
5x + 3y - 4z = c
(b) 2x + y - z = a
2 y + 3 z = b
x - z = c
(c) -x + 3y + 2z = -8
x +2 = 2
3x + 3y + az = b
(d) x + ay = 0
y + bz = 0
z + cx = 0
(e) 3x -y + 2z = 3
x + y - z = 2
2x - 2y + 3z = b
(f) x + ay - z = 1
- x + (a - 2)y + z = -1
2x + 2y + (a - 2)z = 1