If x, y, z are different from zero and |(1+x, 1, 1)(1, 1+y, 1)(1, 1, 1+z)| = 0,

Question

If x, y, z are different from zero and \(\begin{vmatrix} 1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z \end{vmatrix}=0,\) then the value of x^-1 + y^-1+z^-1 is

A. xyz

B. x^-1y^-1z^-1

C. - x - y - z

D. –1

Answer 1

Correct answer is D.

x[(1 + y)z + y] -1[- yz] = 0

xz + xyz+ xy + yz = 0 (divide by xyz in both side)