|[x+y,y+z,z+x],[z,x,y],[-3,-3,-3]|

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

Show that |(x+y,y+z,z+x),(y+z,z+x,x+y),(z+x,x+y,y+z)|=2[3xyz-x^(3)-y^(3)-z^(3)]

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

det[[y+z,z+x,x+yy+z,x+y,y+zx+x,x+y,z+x]]=2det[[x,y,zy,z,xz,x,y]]=-2(x^(3)+y^(3)+z^(3)-3xyz)

det[[y+z,z+x,x+yy+z,x+y,y+zx+x,x+y,z+x]]=2det[[x,y,zy,z,zz,x,y]]=-2(x^(3)+y^(3)+z^(3)-3xyz)