1 a1 0 ...0 0
-1 1-a1 a2 ...0 0
0 -1 1-a2...0 0
....
0 0 0 ...1-an-1 an
0 0 0 ...-1 1-an
r1+r2+...+rn -- 所有行都加到第1行
0 0 0 ...0 1
-1 1-a1 a2 ...0 0
0 -1 1-a2...0 0
....
0 0 0 ...1-an-1 an
0 0 0 ...-1 1-an
按第1行展开
D = (-1)^(1+n) * [下三角行列式,主对角线上都是 -1 ]
= (-1)^(1+n) * (-1)^(n-1)
= 1.