计算行列式A=|1,2,3,41,0,1,23,-1,-1,01,2,0,-5|

Question

计算行列式A=|1,2,3,4 1,0,1,2 3,-1,-1,0 1,2,0,-5|

Answer 1

1 2 3 4
1 0 1 2
3 -1 -1 0
1 2 0 -5
c4-c1-c3, c3-c1
1 2 2 0
1 0 0 0
3 -1 -4 -2
1 2 -1 -6
按第2行展开 D=(-1)^(2+1)*
2 2 0
-1 -4 -2
2 -1 -6
c2-c1
2 0 0
-1 -3 -2
2 -3 -6
D = -2*
-3 -2
-3 -6
= -2*(18-6)
= -24.
注: c4-c1-c3 可看作两次变换 c4-c1, c4-c3.
目的是同时化2个元素为0 (a14和a24)