线性代数求n阶行列式 计算n阶行列式：a b b ...bb a b ...bb b a ...b...........

|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)