Q. If $\left| \begin{matrix} x & y & z \\ - x & y & z \\ x & - y & z \end{matrix} \right| = kxyz,$ then $k$ is equal to
A) 1
B) 3
C) 4
D) 2
Explanation
(c)
$\left| \begin{matrix}
x & y & z \\
- x & y & z \\
x & - y & z
\end{matrix} \right| = \left| \begin{matrix}
x & y & z \\
- x & y & z \\
0 & 0 & 2z
\end{matrix} \right|$ $\lbrack R_{3} \rightarrow R_{3} + R_{2}\rbrack$
$= 2z(xy + xy) = 4xyz$
On comparing with $kxyz$, we get $k = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.