Question

求非齐次线性方程组2X1+7X2+3X3+X4=6 3X1+5X2+2X3+2X4=4 9X1+4X2+X3+7X4=2的通解

Answer 1

解:
增广矩阵
=
2
7
3
1
6
3
5
2
2
4
9
4
1
7
2
r3-3r2,r2-r1
2
7
3
1
6
1
-2
-1
1
-2
0
-11
-5
1
-10
r1-2r2
0
11
5
-1
10
1
-2
-1
1
-2
0
-11
-5
1
-10
r3+r1,r1*(1/11),r2+2r1
0
1
5/11
-1/11
10/11
1
0
-1/11
9/11
-2/11
0
0
0
0
0
交换行
(不交换也行)
1
0
-1/11
9/11
-2/11
0
1
5/11
-1/11
10/11
0
0
0
0
0
方程组的通解为:
(-2/11,10/11,0,0)'+c1(1,-5,11,0)'+c2(9,-1,0,11)'.