`|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]|=?`

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

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

Without expanding the determinant, show that : (frac{1}{x}+frac{1}{y}+frac{1}{z}+1) is a factor of : |[[1+x,1,1],[1,1+y,1],[1,1,1+z]]|

Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

If D=|1 1 1 1 1+x1 1 1 1+y|"f o r"x!=0, y!=0 then D is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

If X-Y=[1 1 1 1 1 0 1 0 0] and X+Y=[3 5 1-1 1 4 11 8 0] , find X and Y .

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

[[1,-1,1],[2,-3,2],[1,3,-1]][[x],[y],[z]]=[[1],[-1],[1]] ,then [[x],[y],[z]] is equal to