解行列式 0 0 ...0 1 0 0 0 ...2 0 0 ........n-1 0 ..0 0 0 0 0 ..0 0 n

问题描述:

解行列式 0 0 ...0 1 0 0 0 ...2 0 0 ........n-1 0 ..0 0 0 0 0 ..0 0 n

是这样子吧:0 0 ...0 1 0 0 0 ...2 0 0 ......n-1 0 ...0 0 0 0 0 ..0 0 n由定义,行列式 = (-1)^t n!t为排列 (n-1)(n-2)...21n 的逆序数.t = n-2+n-3+...+1 = (n-1)(n-2)/2所以行列式 = (-1)^[(n-1)(n-2)/2] n!...