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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
What positive value of $x$ makes the following pair of determinants equal? $\ \left|\begin{array}{cc} 2 x & 3 \\ 5 & x \end{array}\right|,\left|\begin{array}{cc} 16 & 3 \\ 5 & 2 \end{array}\right| $
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Answer

We have, $\left|\begin{array}{rr}2 x & 3 \\ 5 & x\end{array}\right|=\left|\begin{array}{rr}16 & 3 \\ 5 & 2\end{array}\right|$
$ \Rightarrow 2 x^2-15=32-15 $
$\Rightarrow 2 x^2=32 $
$\Rightarrow x^2=16$
$\Rightarrow x=4[\because x>0] $

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