线性代数:计算下列n阶行列式(3),
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线性代数:计算下列n阶行列式(3),
![](http://img.wesiedu.com/upload/2/ae/2aebb825aa09720b234369da49f3041f.jpg)
![](http://img.wesiedu.com/upload/2/ae/2aebb825aa09720b234369da49f3041f.jpg)
![线性代数:计算下列n阶行列式(3),](/uploads/image/z/17390070-54-0.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%E8%AE%A1%E7%AE%97%E4%B8%8B%E5%88%97n%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%283%29%2C)
解: D =
ri-r(i+1), i=1,2,...,n-1
0 1 1 ... 1 1
0 1-x 1 ... 1 1
0 0 1-x ... 1 1
... ...
0 0 0 ...1-x 1
1 x x ... x 1
按第1列展开
D = (-1)^(n+1)*
1 1 ... 1 1
1-x 1 ... 1 1
0 1-x ... 1 1
.. ...
0 0 ...1-x 1
ri-r(i+1), i=1,2,...,n-2
x 0 ... 0 0
1-x x ... 0 0
0 1-x ... 0 0
... ...
0 0 ...1-x 1
D = (-1)^(n+1) x^(n-2).
ri-r(i+1), i=1,2,...,n-1
0 1 1 ... 1 1
0 1-x 1 ... 1 1
0 0 1-x ... 1 1
... ...
0 0 0 ...1-x 1
1 x x ... x 1
按第1列展开
D = (-1)^(n+1)*
1 1 ... 1 1
1-x 1 ... 1 1
0 1-x ... 1 1
.. ...
0 0 ...1-x 1
ri-r(i+1), i=1,2,...,n-2
x 0 ... 0 0
1-x x ... 0 0
0 1-x ... 0 0
... ...
0 0 ...1-x 1
D = (-1)^(n+1) x^(n-2).