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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Find the values of $x$ for which $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$.
  • A
    $2 \sqrt{2}$
  • B
    $-2 \sqrt{2}$
  • C
    3
  • ✓
    both (a) and (b)
✓

Answer

Correct option: D.
both (a) and (b)
(d) : We have, $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$
$
\Rightarrow \quad 3-x^2=3-8 \quad \Rightarrow \quad x^2=8 \text {. Hence, } x= \pm 2 \sqrt{2}
$

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