Question

求行列式D2n=a 0 0 ... 0 0 b,0 a 0 ... 0 b 0,0 0 a ...

求行列式D2n=a 0 0 ... 0 0 b,0 a 0 ... 0 b 0,0 0 a ... b 0 0, ... 0 0 b ... a 0 0,0 b 0 ... 0 a 0,b 0 0 ... 0 0 a.

Answer 1

a b 0 0.....0
0 a b 0.....0
0 0 a b.....0
. . . . .
b 0 0 0..... a

由行列式的定义, 只有两项不等于0
D = a^n + (-1)^t(234...n1) b^n
= a^n + (-1)^(n-1) b^n.

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