非齐次线性方程组X1-5X2+2X3-3X4=11 5X1+3X2+6X3-X4=-1 2X1+4X2+2X3+X4=-

增广矩阵 =
1 -5 2 -3 11
5 3 6 -1 -1
2 4 2 1 -6
r2-5r1,r3-2r1
1 -5 2 -3 11
0 28 -4 14 -56
0 14 -2 7 -28
r2-2r3,r3*(1/14)
1 -5 2 -3 11
0 0 0 0 0
0 1 -1/7 1/2 -2
r1+5r3
1 0 9/7 -1/2 1
0 0 0 0 0
0 1 -1/7 1/2 -2
所以通解为:(1,-2,0,0)'+c1(-9,1,7,0)'+c2(1,-1,0,2),c1,c2 为任意常数.