线性代数求n阶行列式 急急急!
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线性代数求n阶行列式 急急急!
计算n阶行列式:
a b b ... b
b a b ... b
b b a ... b
... ... ... ... ...
b b b ... a
计算n阶行列式:
a b b ... b
b a b ... b
b b a ... b
... ... ... ... ...
b b b ... a
![线性代数求n阶行列式 急急急!](/uploads/image/z/4863278-38-8.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E6%B1%82n%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F+%E6%80%A5%E6%80%A5%E6%80%A5%21)
|a b b ...b|
|b a b ...b|
|b b a ...b|
|...............|
|b b b ...a|
=
|a+(n-1)b a+(n-1)b a+(n-1)b ...a+(n-1)b|
|b a b ...b |
|b b a ...b |
|...............|
|b b b ....a |
=
|b b b ...b|
|b a b ...b|
|b b a ...b| × a+(n-1)b × 1/b
|...............|
|b b b ...a|
=
|b b b ...b|
|0 a-b 0 ...0|
|0 0 a-b ...0| × [a+(n-1)b] × 1/b
|...............|
|0 0 0 ...a-b|
=
[a+(n-1)b] × (a-b)^(n-1)
|b a b ...b|
|b b a ...b|
|...............|
|b b b ...a|
=
|a+(n-1)b a+(n-1)b a+(n-1)b ...a+(n-1)b|
|b a b ...b |
|b b a ...b |
|...............|
|b b b ....a |
=
|b b b ...b|
|b a b ...b|
|b b a ...b| × a+(n-1)b × 1/b
|...............|
|b b b ...a|
=
|b b b ...b|
|0 a-b 0 ...0|
|0 0 a-b ...0| × [a+(n-1)b] × 1/b
|...............|
|0 0 0 ...a-b|
=
[a+(n-1)b] × (a-b)^(n-1)