Question

用基础解系表示下面非齐次线性方程的全部解

x1 - x2 - x3 + x4 = 0 x1 + x2 - x3 - 3 * x4 = 2 x1 - 2 * x2 - x3 + 3 * x4 = -1

Answer 1

增广矩阵=
1
-2
-1
1
0
1
1
-1
-3
2
1
-2
-1
3
-1
用初等行变换化为
1
0
-1
0
1/2
0
1
0
0
0
0
0
0
1
-1/2
方程组的全部解为:
(1/2,0,0,-1/2)^T+k(1,0,1,0)^T