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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
For which value of $x,$ are the determinants $\left|\begin{array}{ll}2 x & -3 \\ 5 & x\end{array}\right|$ and $\left|\begin{array}{cc}10 & 1 \\ -3 & 2\end{array}\right|$ equal?
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Answer

$\begin{array}{l}\text {Since, }\left|\begin{array}{cc}2 x & -3 \\ 5 & x\end{array}\right|=\left|\begin{array}{ll}10 & 1 \\ -3 & 2\end{array}\right| \end{array} $
$ \Rightarrow 2 x^2+15=20+3 $
$\Rightarrow 2 x^2=23-15=8  $
$ \Rightarrow x^2=4 $
$\Rightarrow x= \pm 2$

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