D3=0````````0 1 0 0````````2 0 0 ` ` ` ` ` ` ` ` ` ` ` ` N-1`````0 0 0 0````````0 0 N 计算行列式,

题目

D3=0````````0 1 0 0````````2 0 0 ` ` ` ` ` ` ` ` ` ` ` ` N-1`````0 0 0 0````````0 0 N 计算行列式,

答案

这个按定义做
每行每列恰取一个数相乘,得 1*2*3*.*n = n!(阶乘).
其符号 = (-1)^t,t是列标排列的逆序数,
排列是 (n-1) (n-2) ...1 n
逆序数为 :n(n-1)/2
所以行列式 = (-1)^[n(n-1)/2] n!