If \(\begin{vmatrix}3 & -4\\ 2 & 1\end{vmatrix}=\begin{vmatrix}2x & 5\\ 1 & x\end{vmatrix}\) then \(|x|\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2\sqrt{2}\)
A 2 × 2 determinant is \(\begin{vmatrix}a & b\\ c & d\end{vmatrix} = ad - bc\).
Left side:
\(3 \times 1 - (-4)\times 2 = 3 + 8 = 11\)
Right side:
\(2x \times x - 5 \times 1 = 2x^2 - 5\)
Equating:
\(2x^2 - 5 = 11\)
\(x^2 = 8\)
\(|x| = \sqrt{8} = 2\sqrt{2}\)
NCERT Exemplar:
Determinants
