刘老师,这个行列式怎么求啊?

当a=0时, 显然行列式 = 0.
当a≠0时,
r2 - 1/(2a)r1
2a a^2 0 ... 0 0
0 3a/2 a^2... 0 0
0 1 2a ... 0 0
... ... ...
0 0 0 ... 2a a^2
0 0 0 ... 1 2a
r3- (2/3a)r2
2a a^2 0 ... 0 0
0 3a/2 a^2... 0 0
0 0 4a/3... 0 0
... ... ...
0 0 0 ... 2a a^2
0 0 0 ... 1 2a
. (依次类推)
2a a^2 0 ... 0 0
0 3a/2 a^2... 0 0
0 0 4a/3... 0 0
... ... ... ...
0 0 0 ...na/(n-1) a^2
0 0 0 ... 0 (n+1)a/n
行列式 = 2a* 3a/2*4a/3*...*na/(n-1)*(n+1)a/n
= (n+1)a^n.
也可以将行列式转置一下, 用类似的方法计算.
这个行列式是个考研题