If \(A = \begin{bmatrix}2 & 4\\x & \displaystyle\frac{-1}{2}\end{bmatrix}\) and A is singular, then x is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-\displaystyle\frac{1}{4}\)
A singular matrix has determinant 0:
\( \displaystyle |A| = 2\times\left(-\frac{1}{2}\right) - 4x = 0 \)
\(-1 - 4x = 0\)
\( \displaystyle x = -\frac{1}{4} \)