If \(\det\begin{pmatrix}2x&5\\8&x\end{pmatrix} =\det\begin{pmatrix}6&-2\\1&1\end{pmatrix}\), then the value of \(x\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\pm 2\sqrt{6}\)
Expanding each 2 × 2 determinant as \(ad - bc\):
\(2x \cdot x - 5 \cdot 8 = 6 \cdot 1 - (-2) \cdot 1\)
\(2x^2 - 40 = 8\)
\(x^2 = 24\)
\(x = \pm\sqrt{24} = \pm 2\sqrt{6}\)