Q. The value of the determinant$\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1 - x & 1 \\ 1 & 1 & 1 + y \end{matrix} \right|$is equal to
A) $3 - x + y$
B) $(1 - x)(1 + y)$
C) $xy$
D) $- xy$
Explanation
(d)
$\left| \begin{matrix}
1 & 1 & 1 \\
1 & 1 - x & 1 \\
1 & 1 & 1 + y
\end{matrix} \right| = \left| \begin{matrix}
1 & 0 & 0 \\
1 & - x & 0 \\
1 & 0 & y
\end{matrix} \right|\left\lbrack \begin{array}{r}
C_{2} \rightarrow C_{2} - C_{1} \\
C_{3} \rightarrow C_{3} - C_{1}
\end{array} \right\rbrack$
$= - xy$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.