If \(\begin{vmatrix} 2x & 3\\ 5 & x\end{vmatrix} = \begin{vmatrix} 16 & 3\\ 5 & 2\end{vmatrix}\) the value of x is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x = \pm 4\)
A 2 × 2 determinant is
\( \begin{vmatrix} a & b\\ c & d\end{vmatrix} = ad - bc \)
Left side:
\(2x \cdot x - 3 \cdot 5 = 2x^2 - 15\)
Right side:
\(16 \cdot 2 - 3 \cdot 5 = 32 - 15 = 17\)
Equating the two:
\(2x^2 - 15 = 17\)
\(2x^2 = 32\)
\(x^2 = 16\)
\(x = \pm 4\)