系数矩阵 A =
[1 1 -2 3]
[2 1 -6 4]
[3 2 -8 7]
[1 -1 -6 -1]
行初等变换为
[1 1 -2 3]
[0 -1 -2 -2]
[0 -1 -2 -2]
[0 -2 -4 -4]
行初等变换为
[1 0 -4 1]
[0 1 2 2]
[0 0 0 0]
[0 0 0 0]
x1=4x3-x4
x2=-2x3-2x4
得基础解系 (4, -2, 1, 0)T, (1, 2, 0, -1)T.
通解 x=k(4, -2, 1, 0)T+c(1, 2, 0, -1)T.