1.解: 系数矩阵=
1 -1 3
3 1 1
-1 2 -5
r2-3r1, r3+r1
1 -1 3
0 4 -8
0 1 -2
r1+r3,r2-4r3
1 0 1
0 0 0
0 1 -2
方程组的解为: c(-1,2,1)^T.
2.
解: 增广矩阵 =
1 -1 2 -1
3 1 0 2
1 3 -4 4
r2-3r1,r3-r1
1 -1 2 -1
0 4 -6 5
0 4 -6 5
r3-r2,r2*(1/4),r1+r2
1 0 1/2 1/4
0 1 -3/2 5/4
0 0 0 0
方程组的解为: (1/4,5/4,0)^T+c(-1,3,2)^T.