计算n阶行列式D,其中Xi不等于0,i=1,2,...n,第一行为1,2,...n-1,n+Xn,第二行为1,2,...(n-1)+Xn-1,n,

用加边法.D=
1 1 2 ...n-1 n
0 1 2 ...n-1 n+Xn
0 1 2 ...n-1+Xn-1 n
......
0 1 2+X2...n-1 n
0 1+X1 2...n-1 n
所有行减第1行得
1 1 2 ...n-1 n
-1 0 0 ...0 Xn
-1 0 0 ...Xn-1 0
-1 ......
-1 0 X2 ...0 0
-1 X1 2 ...0 0
c1+ (1/x1)c2 + (1/x2)c3 + ...+ (1/xn)cn+1
M 1 2 ...n-1 n
0 0 0 ...0 Xn
0 0 0 ...Xn-1 0
0 ......
0 0 X2 ...0 0
0 X1 2 ...0 0
其中 M = 1+ 1/x1 + 2/x2 + ...+ n/xn
按第1列展开得 D=(-1)^[n(n-1)/2]x1x2...xn(1+ 1/x1 + 2/x2 + ...+ n/xn)