怎么将四阶行列式轮换为三阶的?求详细的步骤及具体应用的知识点如1110110110110111

Question

怎么将四阶行列式轮换为三阶的?求详细的步骤及具体应用的知识点 如 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1

Answer 1

1 1 1 0
1 1 0 1
1 0 1 1
0 1 1 1
c1+c2+c3+c4
3 1 1 0
3 1 0 1
3 0 1 1
3 1 1 1
ri-r4,i=1,2,3
0 0 0 -1
0 0 -1 0
0 -1 0 0
3 1 1 1
行列式 = (-1)^(3+2+1) *3* (-1)^3 = -3