解: 增广矩阵 (A,b)=
1 2 0 -4 -3
1 -1 -4 9 22
2 -3 1 5 -3
3 -2 -5 1 3
r1-r2,r3-2r2,r4-3r2
0 3 4 -13 -25
1 -1 -4 9 22
0 -1 9 -13 -47
0 1 7 -26 -63
r1-3r4,r2+r4,r3+r4
0 0 -17 65 164
1 0 3 -17 -41
0 0 16 -39 -110
0 1 7 -26 -63
r1+r3
0 0 -1 26 54
1 0 3 -17 -41
0 0 16 -39 -110
0 1 7 -26 -63
r2+3r1,r3+16r1,r4+7r1
0 0 -1 26 54
1 0 0 61 121
0 0 0 377 754
0 1 0 156 315
r3*(1/377), r1-26r3,r2-61r3,r4-156r3
0 0 -1 0 2
1 0 0 0 -1
0 0 0 1 2
0 1 0 0 3
r1*(-1), 交换行
1 0 0 0 -1
0 1 0 0 3
0 0 1 0 -2
0 0 0 1 2
方程组的解为 (-1,3,-2,2)^T.