四阶行列式第一行0，y，0，x第二行x，0，y，0第三行0，x，0，y，第四行y，0，x，0.怎么求.

Question

四阶行列式第一行0，y，0，x第二行x，0，y，0第三行0，x，0，y，第四行y，0，x，0.怎么求 .

Answer 1

| 0 y 0 x | | x 0 y 0 | | 0 x 0 y | | y 0 x 0 | = | 0 y 0 x | | x+y 0 x+y 0 | | 0 x 0 y | | y 0 x 0 | = | 0 y 0 x | | 1 0 1 0 | | 0 x 0 y |(x+y) | y 0 x 0 | = | 0 x+y 0 x+y | | 1 0 1 0 | | 0 x 0 y |(x+y) | y 0 x 0 | = | 0 1 0 1 | | 1 0 1 0 | | 0 x 0 y |(x+y)(x+y) | y 0 x 0 | = | 0 1 0 1 | | 1 0 1 0 | | 0 0 0 y-x |(x+y)(x+y) | y 0 x 0 | = | 0 1 0 1 | | 1 0 1 0 | | 0 0 0 1 |(x+y)(x+y)(y-x) | y 0 x 0 | = | 0 1 0 | | 1 0 1 |(x+y)(x+y)(y-x)(-1) | y 0 x | = | 1 1 |(x+y)(x+y)(y-x)(-1)(-1) | y x | = (x-y)(x+y)(x+y)(y-x)(-1)(-1) = -(x-y)(x+y)
记得采纳啊