[问题2014A05] (1) 设 \(x_1,x_2\cdots,x_n,x\) 都是未定元, \(s_k=x_1^k+x_2^k+\cdots+x_n^k\,(k\geq 1)\), \(s_0=n\), 试求下列行列式的值:
\[|A|=\begin{vmatrix} s_0 & s_1 & \cdots & s_{n-1} & 1 \\ s_1 & s_2 & \cdots & s_n & x \\ \vdots & \vdots & \vdots & \vdots & \vdots \\ s_n & s_{n+1} & \cdots & s_{2n-1} & x^n \end{vmatrix}.\]
(2) 设 \(A=(a_{ij})\) 为 \(n\) 阶方阵, 试求下列行列式的值:
\[\begin{vmatrix} a_{11} & & & a_{12} & & \cdots & & a_{1n} & & \\ & \ddots & & & \ddots & & \ddots & & \ddots & \\ & & a_{11} & & & a_{12} & & \cdots & & a_{1n} \\ a_{21} & & & a_{22} & & \cdots & & a_{2n} & & \\ & \ddots & & & \ddots & & \ddots & & \ddots & \\ & & a_{21} & & & a_{22} & & \cdots & & a_{2n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & & & a_{n2} & & \cdots & & a_{nn} & & \\ & \ddots & & & \ddots & & \ddots & & \ddots & \\ & & a_{n1} & & & a_{n2} & & \cdots & & a_{nn} \\ \end{vmatrix}.\]
[问题2014A05] 复旦高等代数 I（14级）每周一题（第七教学周）
原文：http://www.cnblogs.com/torsor/p/4050041.html