Q. The value of the determinant$\left| \begin{matrix} y + z & x & x \\ y & z + x & y \\ z & z & x + y \end{matrix} \right|$is equal to
A) 6$xyz$
B) $xyz$
C) $4xyz$
D) $xy + yz + zx$
Explanation
(c)
Applying $R_{1} \rightarrow R_{1} - \left( R_{2} + R_{3} \right)$, we get
$\left| \begin{matrix}
0 & - 2z & - 2y \\
y & z + x & y \\
z & z & x + y
\end{matrix} \right|$
$= 2z\left( xy + y^{2} - yz \right) - 2y(yz - z^{2} - xz)$
$= 2xyz + 2y^{2}z - 2yz^{2} - 2y^{2}z + 2yz^{2} + 2xyz$
$= 4xyz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.