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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $x, y, z$ are all 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:
Solution
Expand the determinant: $(1+x)(1+y)(1+z) - (1+x) - (1+y) - (1+z) + 2 = 0$ Simplify: $xyz(x^{-1} + y^{-1} + z^{-1}) + ... = 0$ Final result gives $\boxed{x^{-1} + y^{-1} + z^{-1} = -1}$ $\boxed{\text{Answer: (D) -1}}$Online Test Series, Information About Examination,
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