Question

3道简答的齐次线性方程组题···求一个基础解析·········谢谢了··

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Answer 1

(1)系数矩阵 A =
1 -2 4 -7
2 1 -2 1
3 -1 2 -4

r2-2r1,r3-3r1
1 -2 4 -7
0 5 -10 15
0 5 -10 17

r3-r2,r2*(1/5),r3*(1/2)
1 -2 4 -7
0 1 -2 3
0 0 0 1

r2-3r3,r1+7r3,r1+2r2
1 0 0 0
0 1 -2 0
0 0 0 1

基础解系为: (0,2,1,0)

(2)系数矩阵 A =
1 -2 1 -1 1
2 1 -1 2 -3
3 -2 -1 1 -2
2 -5 1 -2 2
经初等行变换化为
1 0 0 1/2 -7/8
0 1 0 1/2 -5/8
0 0 1 -1/2 5/8
0 0 0 0 0

基础解系为: (-1,-1,1,2,0)',(7,5,-5,0,8)'.

(3)系数矩阵 A =
1 -2 1 1 -1
2 1 -1 -1 1
1 7 -5 -5 5
3 -1 -2 1 -1

经初等行变换化为
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 -1

基础解系为: (0,0,0,1,1)'.

Answer 2

化阶梯型啊！再求秩