增广矩阵=
1 2 -1 2 -1
2 3 2 -1 2
3 4 5 4 t
r3-r1-r2,r2-2r1
1 2 -1 2 -1
0 -1 4 -5 4
0 -1 4 3 t-1
r1+2r2,r3-r2
1 0 7 -8 7
0 -1 4 -5 4
0 0 0 8 t-5
r1+r3,r2*(-1),r3*(1/8)
1 0 7 0 t+2
0 1 -4 5 -4
0 0 0 1 (t-5)/8
r2-5r3
1 0 7 0 t+2
0 1 -4 0 -(5t+7)/8
0 0 0 1 (t-5)/8
参数t取任何值都有解
通解为
(t+2,-(5t+7)/8,(t-5)/8) + k(-7,4,1,0),k为任意数.