Q. If $\mathrm{\Delta} = \left| \begin{matrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ 3 & 9 & 13 \end{matrix} \right|$ and $\mathrm{\Delta}^{'} = \left| \begin{matrix} 7 & 20 & 29 \\ 2 & 5 & 7 \\ 3 & 9 & 13 \end{matrix} \right|$ , then
A) $\mathrm{\Delta}^{'} = 3\mathrm{\Delta}$
B) $\mathrm{\Delta}^{'} = \frac{3}{\mathrm{\Delta}}$
C) $\mathrm{\Delta}^{'} = \mathrm{\Delta}$
D) $\mathrm{\Delta}^{'} = 2\mathrm{\Delta}$
Explanation
(c)
Given that,
$\mathrm{\Delta} = \left| \begin{matrix}
1 & 2 & 3 \\
2 & 5 & 7 \\
3 & 9 & 13
\end{matrix} \right|$
Applying $R_{1} \rightarrow R_{1} + 2R_{3}$
$\mathrm{\Delta} = \left| \begin{matrix}
7 & 20 & 29 \\
2 & 5 & 7 \\
3 & 9 & 13
\end{matrix} \right|$
$\Rightarrow \ \mathrm{\Delta} = \mathrm{\Delta}'$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.