If `(111.1)^x=(11.11)^y=(1.111)^z` then prove that `(1)/(x)-(2)/(y)+(1)/(z)=0`.

Show that : |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xyz(1+(1)/(x)+(1)/(y)+(1)/(z))

If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0 then value of x^(-1)+y^(-1)+z^(-1) is ".........."

If x+y+z=0 then show that abs((1,1,1),(x,y,z),(x^3,y^3,z^3)) = 0.

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

Addition : (1.111)_(2) + (11.11)_(2) + (111.1)_(2) + (1111)_(2)

If |{:(x-1,1,1),(1,x+1,1),(-1,1,x+1):}|=0 , find the value of x.

If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

If [[1,1,1],[1,1+x,1],[1,1,1+y]]=0 what are x and y?