If \(\begin{vmatrix}2x & 5\\ 8 & x\end{vmatrix}=\begin{vmatrix}6 & -2\\ 7 & 3\end{vmatrix}\), then the value of x is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −6 or 6
A 2 × 2 determinant is \(\begin{vmatrix}a & b\\ c & d\end{vmatrix} = ad - bc\).
Left side:
\(2x \times x - 5 \times 8 = 2x^2 - 40\)
Right side:
\(6 \times 3 - (-2) \times 7 = 18 + 14 = 32\)
Equating:
\(2x^2 - 40 = 32\)
\(x^2 = 36\)
\(x = -6 \text{ or } x = 6\)
Both values satisfy the equation, because x appears only as x2.
NCERT Exemplar:
Determinants
