If | , * 20 c 4&1 2&1 , |^2 = | , * 20 c 3&2 1&x , | - | , * 20 c… - Vidyadip

MCQ

If ${\left| {\,\begin{array}{*{20}{c}}4&1\\2&1\end{array}\,} \right|^2} = \left| {\,\begin{array}{*{20}{c}}3&2\\1&x\end{array}\,} \right| - \left| {\,\begin{array}{*{20}{c}}x&3\\{ - 2}&1\end{array}\,} \right|$, then $ x =$

A
$-14$
B
$2$
✓
$6$
D
$7$

✓

Answer

Correct option: C.

$6$

c
(c) $\left| {\,\begin{array}{*{20}{c}}4&1\\2&1\end{array}\,} \right|\,\left| {\,\begin{array}{*{20}{c}}4&1\\2&1\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}3&2\\1&x\end{array}\,} \right| - \left| {\,\begin{array}{*{20}{c}}x&3\\{ - 2}&1\end{array}\,} \right|$

$ = \left| {\,\begin{array}{*{20}{c}}{17}&9\\9&5\end{array}\,} \right| = (3x - 2) - (x + 6)$

==> $85 - 81 = 2x - 8$

==> $4 + 8 = 2x$

==> $x = 6$.

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