Solve each system, giving the solution set in vector notation. Identify the particular solution and the solution

Question:

Solve each system, giving the solution set in vector notation. Identify the particular solution and the solution of the homogeneous system.
(a) 2x + y - z = 1
4x - y = 3
(b) x - z = 1
y + 2z - w = 3
x + 2y + 3z - w = 7
(c) x - y + z = 0
y + w = 0
3x - 2y + 3z + w = 0
-y - w = 0
(d) a + 2b + 3c + d - e = 1
3a - b + c + d + e = 3