If \(\begin{vmatrix}x & 4\\ 3 & 2x\end{vmatrix} = \begin{vmatrix}6 & 2\\ -1 & 6\end{vmatrix}\), then the value of x is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\pm 5\)
A 2 × 2 determinant is the product of the main diagonal minus the product of the other diagonal.
Left side:
\( x \times 2x - 4 \times 3 = 2x^2 - 12 \)
Right side:
\( 6 \times 6 - 2 \times (-1) = 36 + 2 = 38 \)
Equating the two:
\( 2x^2 - 12 = 38 \)
\( 2x^2 = 50 \)
\( x^2 = 25 \)
\( x = \pm 5 \)