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

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)

晕~~~~~~~~~~~~~~

拉普拉斯展开法则求解

题目很简单，不过过程打出来是在是有点....复杂

| x y x+y| （第一行，第二行加到第一行上。提起公因式）
| y x+y x| ============================================
| y x+y x|
|1 y x+y|
==(2x+2y)|1 x+y x|
|1 x y |
| 1 y ...