For each of the following homogeneous systems, find a set of basic solutions and express the general solution as a linear combination of these basic solutions.
(a) x1 + 2x2 - x3 + 2x4 +x5=0
x1 + 2x2 + 2x3 +x5=0
2x1 + 4x2 - 2x3 + 3x4 +x5 = 0
(b) x1 + 2x2 - x3 + x4 + x5 = 0
- x1 - 2x2 + 2x3 +x5= 0
-x1 - 2x2 + 3x3 + x4 + 3x5 = 0
(c) x1 + x2 - x3 + 2x4 + x5 =0
x1 + 2x2 - x3 + x4 + x5 = 0
2x1 + 3x2 - x3 + 2x4 + x5 = 0
4x1 + 5x2 - 2x3 + 5x4 + 2x5 = 0
(d) x1 + x2 - 2x3 - 2x4 + 2x5 = 0
2x1 + 2x2 - 4x3 - 4x4 + x5 = 0
x1 - x2 + 2x3 + 4x4 + x5 = 0
-2x1 - 4x2 + 8x3 + 10x4 + x5 = 0