求行列式D=|0-1-12,1-102,-12-10,2110|

Question

求行列式D=|0 -1 -1 2,1 -1 0 2,-1 2 -1 0,2 1 1 0|

Answer 1

0 -1 -1 2
1 -1 0 2
-1 2 -1 0
2 1 1 0
r2-r1
0 -1 -1 2
1 0 1 0
-1 2 -1 0
2 1 1 0
r3+r2,r4-r2
0 -1 -1 2
1 0 1 0
0 2 0 0
1 1 0 0
c2-c1
0 -1 -1 2
1 -1 1 0
0 2 0 0
1 0 0 0
--这是斜上三角行列式, 等于 (-1)^[n(n+1)/2]*斜对角线上的元素的乘积
= 2*1*2*1
= 4