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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants2 Marks
Question
Find the value of x, if:
$\begin{vmatrix}2&3\\4&5\end{vmatrix}=\begin{vmatrix}\text{x}&3\\2\text{x}&5\end{vmatrix}$
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Answer

Given, $\begin{vmatrix}2&3\\4&5\end{vmatrix}=\begin{vmatrix}\text{x}&3\\2\text{x}&5\end{vmatrix}$$\Rightarrow2\times5-3\times4=\text{x}\times5-3\times2\text{x}$
$\Rightarrow10-12=5\text{x}-6\text{x}$
$\Rightarrow-2=-\text{x}$
$\Rightarrow\text{x}=2$

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