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),

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).