D=(n-1)乘以-1的(n-1)次方
将第一列*(-1)分别加到后面各列,得
0 1 1 1 1... 1 1
1 -1 0 0 0... 0 0
1 0 -1 0 0... 0 0
1 0 0 -1 0... 0 0
1 0 0 0 -1... 0 0
.
1 0 0 0 0...-1 0
1 0 0 0 0... 0 -1
再将第2至第n行分别加到第1行,得
n-1 0 0 0 0... 0 0
1 -1 0 0 0... 0 0
1 0 -1 0 0... 0 0
1 0 0 -1 0... 0 0
1 0 0 0 -1... 0 0
.
1 0 0 0 0...-1 0
1 0 0 0 0... 0 -1
所以,D=(n-1)乘以-1的(n-1)次方