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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
If $\left|\begin{array}{cc} {x} & {2} \\ {18} & {x} \end{array}\right|=\left|\begin{array}{cc} {6} & {2} \\ {18} & {6} \end{array}\right|$ , then $x$ is equal to
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Answer

We have $\left|\begin{array}{ll} {x} & {2} \\ {18} & {x} \end{array}\right|=\left|\begin{array}{ll} {6} & {2} \\ {18} & {6} \end{array}\right|$
We know that determinant of $A$ is calculated as $|A|=\left|\begin{array}{ll} {a} & {b} \\ {c} & {d} \end{array}\right| = ad - bc$
$\Rightarrow x(x) – 2(18) = 6(6) – 2(18)$
$\Rightarrow x^2 - 36 = 36 – 36$
$\Rightarrow x^2 =36 – 36 + 36$
$\Rightarrow x^2 = 36$
$\Rightarrow x = \pm6$

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