If `Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|`,then

Value of |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

Prove that : |{:(x-y-z ,2x, 2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|=(x+y+z)^(3)

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)

x-y+z=1 2x+y-z=2 x-2y-z=4

Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2x y z(x+y+z)^3 .

(x+y+z) is fator of : {:|(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y)|

Prove that |{:(,x+y+2z,x,y),(,z,y+z+2z,y),(,z,x,z+x+2y):}|=2(x+y+z)^(3) .