计算5阶行列式,第一行1,2,3,4,5第二行2,3,4,5,1第三行3,4,5,1,2,第四行4,5,1,2,3第五行5,1,2,3,4

Question

计算5阶行列式,第一行 1,2,3,4,5第二行2,3,4,5,1第三行3,4,5,1,2,第四行4,5,1,2,3第五行5,1,2,3,4

Answer 1

D=15*|1 1 1 1 1|
2 3 4 5 1
3 4 5 1 2
4 5 1 2 3
5 1 2 3 4
=15*|1 0 0 0 0|
2 1 2 3 -1
3 1 2 -2 -1
4 1 -3 -2 -1
5 -4 -3 -2 -1
=15*|1 0 0 0 0|
2 1 2 3 -1
1 0 0 -5 0
1 0 -5 0 0
1 -5 0 0 0 【r5-r4、r4-r3、r3-r2】
=15*|1 0 0 0 0|
1 -5 0 0 0
1 0 -5 0 0
1 0 0 -5 0
2 1 2 3 -1
=3*5^4
=1875