What positive value of x makes the following pair of determinants… - Vidyadip

MCQ

What positive value of $x$ makes the following pair of determinants equal? $\left|\begin{array}{cc}2 x & 3 \\5 & x\end{array}\right|, \left|\begin{array}{cc}16 & 3 \\5 & 2\end{array}\right|$

A
$1$
B
$2$
C
$3$
✓
$4$

✓

Answer

Correct option: D.

$4$

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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