Solution Spaces of Homogenous Linear Algebraic Systems
Solve the linear systems given in Problems 1-3 and determine their solution spaces.
1.
x1 - x2 + 4x4 + 2x5 - x6 = 0
2x1 - 2x2 + x3 + 2x4 + 4x5 - x6 = 0
2.
2x1 - 2x2 + 4x3 - 2x4 = 0
2x1 + x2 + 7x3 + 4x4 = 0
x1 - 4x2 - x3 + 7x4 = 0
4x1 - 12x2 - 20x4 = 0
3.
3x1 + 6x3 + 3x4 + 9x5 = 0
x1 + 3x2 - 4x3 - 8x4 + 3x5 = 0
x1 - 6x2 + 14 x3 + 19x4 + 3x5 = 0