For what value of \( \mu \), \( \begin{bmatrix} 5 & \mu-7\\ 12 & 9\end{bmatrix} \) is a singular matrix?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10.75
A square matrix is singular when its determinant is 0:
\( \displaystyle \begin{vmatrix} 5 & \mu-7\\ 12 & 9\end{vmatrix}=45-12(\mu-7)=0 \)
\( \displaystyle 12\mu-84=45 \)
\( \displaystyle 12\mu=129 \)
\( \displaystyle \mu=10.75 \)