The matrix \(\begin{bmatrix}x & 4\\ 3 & x + 1\end{bmatrix}\) is singular if
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(x = 3\) or \(x = -4\)
A matrix is singular when its determinant is zero:
\(x(x + 1) - 4 \cdot 3 = 0\)
\(x^{2} + x - 12 = 0\)
\((x - 3)(x + 4) = 0\)
So \(x = 3\) or \(x = -4\), and both values make the determinant zero.