行列式|A+B|怎么求?设4阶行列式|A|=det(a1,a2,a3,a4)=3,|B|=det(b1,a2,a3,a4)=-5,求|A+B|

问题描述:

行列式|A+B|怎么求?
设4阶行列式|A|=det(a1,a2,a3,a4)=3,|B|=det(b1,a2,a3,a4)=-5,求|A+B|

det(a1+b1 a2+b2 a3+b3 a4+b4)
加完了求

det(a1+b1,a2+a2,a3+b3,a4+b4)
=det(a1,a2+a2,a3+b3,a4+b4)+det(b1,a2+a2,a3+b3,a4+b4)
=8det(a1,a2,a3,a4)+8det(b1,a2,a3,a4)
=24-40
=-16