Question

求四阶行列式1234/2341/3412/4123

Answer 1

1 2 3 4

2 3 4 1

3 4 1 2

4 1 2 3

=1*[3*(1*3-2*2)-4*(4*3-2*1)+1*(4*2-1*1)]-2*[2*(1*3-2*2)-4*(3*3-2*4)+1*(3*2-1*4)]+3*[2*(4*3-2*1)-3*(3*3-2*4)+1*(3*1-4*4)]-4*[2*(4*2-1*1)-3*(3*2-1*4)+4*(3*1-4*4)]

=1*(-3-40+7)-2*(-2-4+2)+3*(20-3-13)-4*(14-6-52)

=-36+8+12+176

=160