系数矩阵 A =
1 -2 1 -1 1
2 1 -1 2 -3
3 -2 -1 1 -2
2 -5 1 -2 2
r2-2r1,r3-3r1,r4-2r1
1 -2 1 -1 1
0 5 -3 4 -5
0 4 -4 4 -5
0 -1 -1 0 0
r1-2r4,r2+5r4,r3+4r4
1 0 3 -1 1
0 0 -8 4 -5
0 0 -8 4 -5
0 -1 -1 0 0
r3-r2,r2*(-1/8),r1-3r2,r4+r2
1 0 0 1/2 -7/8
0 0 1 -1/2 5/8
0 0 0 0 0
0 -1 0 -1/2 5/8
r4*(-1),交换行得
1 0 0 1/2 -7/8
0 1 0 1/2 -5/8
0 0 1 -1/2 5/8
0 0 0 0 0
基础解系为:(-1,-1,1,2,0)',(7,5,-5,0,8)'.