Question

求解线性代数非齐次线性方程组通解

Answer 1

写出其增广矩阵为
1 2 3 -1 1
3 2 1 -1 1
2 3 1 1 1
2 2 2 -1 1
5 5 2 0 2 r5-r2，r5-r3，r3-r4，r2-3r1，r4-2r1
~
1 2 3 -1 1
0 -4 -8 2 -2
0 1 -1 2 0
0 -2 -4 1 -1
0 0 0 0 0 r1+r4，r2-2r4，r4+2r3，r4*-1
~
1 0 -1 0 0
0 0 0 0 0
0 1 -1 2 0
0 0 6 -5 1
0 0 0 0 0 r1*6，r3*6，r1+r4，r3+r4，交换行次序
~
6 0 0 -5 1
0 6 0 7 1
0 0 6 -5 1
0 0 0 0 0
0 0 0 0 0
于是得到解集为(1/6,1/6,1/6,0,0)^T +c(5,-7,5,6)^T，c为常数

Answer 2

Answer 3