几道线形代数题,求教1.| x y x+y| 3.| x a a a a || y x+y x | | a x a a

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/06 09:31:44

几道线形代数题,求教
1.| x y x+y| 3.| x a a a a |
| y x+y x | | a x a a a |
|x+y x y | | a a x a a |
2.|1 0 a 1 | | a a a x a |
|0 -1 b -1 | | a a a a x |
|-1 -1 c -1 | 5.| 0 .n|
|-1 1 d 0 | | 1 0 .|
4.| a 1 ...1 1 | | 2 .|
| 1 a ...1 1 | | ..|
| ::::| | |
| 1 1 ...a 1 | | n-1 0 |
| 1 1 ...1 a |
6.| 1 1 1 1 |
| 1 3 1 1 |
| 1 1 3 1 |
| 1 1 1 3 |
1.| x y x+y|
| y x+y x|
|x+y x y |
2.|1 0 a 1 |
|0 -1 b -1 |
|-1 -1 c -1 |
|-1 1 d 0 |
3.| x a a a a |
| a x a a a |
| a a x a a |
| a a a x a |
| a a a a x |
4.| a 1 ...1 1 |
| 1 a ...1 1 |
| ::::|
| 1 1 ...a 1 |
| 1 1 ...1 a |

1.
| x y x+y|
| y x+y x|
|x+y x y |
=x*(x+y)*y+y*x*(x+y)+(x+y)*y*x-((x+y)^3+x^3+y^3)
=x^2y+xy^2+yx^2+y^2x+x^2y+xy^2-2x^3-2y^3-3xy^2-3x^2
=-2x^3-2y^3
2
|1 0 a 1 |
|0 -1 b -1|
|-1 -1 c -1|
|-1 1 d 0 |
=0+0+a++0-b-0-0+c=a-b+c,
3.
| x a a a a |
| a x a a a |
| a a x a a |
| a a a x a |
| a a a a x |
=|x+5a a a a a|
|x+5a x a a a|
|x+5a a x a a|
|x+5a a a x a|
|x+5a a a a x|
=|x+5a a a a a|
|0 x a a a|
|0 0 x a a|
|0 0 0 x a|
|0 0 0 0 x|
=x^4*(x+5a)
4
| a 1 ... 1 1 |
| 1 a ... 1 1 |
| : : : : |
| 1 1 ... a 1 |
| 1 1 ... 1 a |
和上题类似,
=（a+n）*(a)^(n-1)

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