if `x ne 0 , y ne 0 ,z ne 0 " and " |{:(1+x,,1,,1),(1+y,,1+2y,,1),(1+z,,1+z,,1+3z):}|=0` then
`x^(-1) +y^(-1) +z^(-1)` is equal to

If x, y, z are all different and not equal to zero and |{:(1+x,,1,,1),(1,,1+y,,1),(1,,1,,1+z):}| = 0 then the value of x^(-1) + y^(-1) + z^(-1) is equal to

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x!=0,y!=0,z!=0 and det[[1+x,1,11+y,1+2y,11+z,1+z,1+3z]]=0, then x^(-1)+y^(-1)+z^(-1) is equal to a.1b.1c.-3d none of these

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

If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0

If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}| =0 then show that 1+xyz=0

If [{:(1,1,1),(1,-2,-2),(1,3,1):}][{:(x),(y),(z):}]=[{:(0),(3),(4):}] , then [{:(x),(y),(z):}] is equal to

If [{:(1,1,1),(1,-2,-2),(1,3,1):}][{:(x),(y),(z):}]=[{:(0),(3),(4):}] , then [{:(x),(y),(z):}] is equal to