For which value of x, are the determinants | ll 2 x & -3 5 & x | and | cc 10 & 1 -3 & 2 | equal?

For which value of x, are the determinants | ll 2 x & -3 5 & x

MCQ

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?

A
$\pm 3$
B
$-3$
✓
$\pm 2$
D
$2$

✓

Answer

Correct option: C.

$\pm 2$

Since, $\left|\begin{array}{cc}2 x & -3 \\ 5 & x\end{array}\right|=\left|\begin{array}{ll}10 & 1 \\ -3 & 2\end{array}\right| $
$ \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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