Question

If $\left| \begin{matrix} 4 & 1 \ 2 & 1 \end{matrix} \right|^{2} = \left| \begin{matrix} 3 & 2 \ 1 & x \end{matrix} \right| - \left| \begin{matrix} x & 3 \

• 2 & 1 \end{matrix} \right|$, then x =

• A. – 14
• B. 2
• C. 6
• D. 7

Answer 1

Answer: (C)

6

Answer 2

$\left| \begin{matrix} 4 & 1 \ 2 & 1 \end{matrix} \right|\left| \begin{matrix} 4 & 1 \ 2 & 1 \end{matrix} \right| = \left| \begin{matrix} 3 & 2 \ 1 & x \end{matrix} \right| - \left| \begin{matrix} x & 3 \

• 2 & 1 \end{matrix} \right|$

17 & 9 \\ 9 & 5 \end{matrix} \right| = (3x - 2) - (x + 6)$$ ⇒ $85 - 81 = 2x - 8$ ⇒ $4 + 8 = 2x$⇒ $x = 6$.