Question

用行列式性质计算下列行列式

x y x+y
y x+y x
x+y x y

Answer 1

c1+c2+c3 第2,3列加到第1列
2(x+y) y x+y
2(x+y) x+y x
2(x+y) x y

r2-r1,r3-r1
2(x+y) y x+y
0 x -y
0 x-y -x

=2(x+y)[-x^2+y(x-y)]
=-2(x+y)(x^2-xy+y^2)