|[x+y,z,1],[y+z,x,1],[z+x,y,1]|=0

Without expanding prove that det[[x+y,z,1y+z,x,1z+x,y,1]]=0

The value of the det. |[x+y,y+z,z+x],[z,x,y],[1,1,1]| is

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

The value of |[x+y, y+z, z+x] , [z,x,y] , [1,1,1]| is

The value of |[[1,x,y+z],[1,y,z+x],[1,z,x+y]]| is

|(x,1,y+z),(y,1,z+x),(z,1,x+y)|=

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

If x, y, z being positive |[1, log _x y,log _x z],[log _y x,1,log _y z],[log _z x,log _z y, 1]|=

If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 then using properties of determinants, show that xyz= -1.