Question

一个行列式的证明|ax+by ay+bz az+bx| |x y z||ay+bz az+bx ax+by|=(a^3+

Answer 1

|ax+by ay+bz az+bx| |ax ay az| |bx by bz| |x ay az| |bx by bz| |x y z| |x y z||ay+bz az+bx ax+by|=|ay az ax|+|by bz bx|=a|y az ax|+|by bz bx|=a*a*a|y z x|+b*b*b|y z x||az+bx ax+by ay+bz| |az ax ay| |bz bx by| |z ax ay| |bz bx by| |z x y| |z x y|