([v)],[z+y,y+z],[z,x],[1,1]quad [z+x],[y],[1]|=0

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

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]|=

The value of the det. |[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

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, 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 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