求非.X1+X2－X3+X4=1 ,X1－X2+X3－3X4＝1,X1－X2－2X3＋3X4=-1/2

增广矩阵 =
1 1 -1 1 1
1 -1 1 -3 1
1 -1 -2 3 -1/2
r3-r2,r2-r1
1 1 -1 1 1
0 -2 2 -4 0
0 0 -3 6 -3/2
r2*(-1/2),r3*(-1/3)
1 1 -1 1 1
0 1 -1 2 0
0 0 1 -2 1/2
r1-r2,r2+r3
1 0 0 -1 1
0 1 0 0 1/2
0 0 1 -2 1/2
所以方程组的通解为 (1,1/2,1/2,0)^T + c(1,0,2,1)^T.