Topic: Engineering Mathematics
For which value of x, will the matrix $\begin{bmatrix} 8 & x & 0 \\ 4 & 0 & 2 \\ 12 & 6 & 0 \end{bmatrix}$ become singular?
- A. 4
- B. 6
- C. 8
- D. 12
Answer: A. 4
Explanation: A matrix becomes singular if its determinant evaluates to zero. Setting the determinant to zero: $8(0 - 12) - x(0 - 24) + 0(24 - 0) = 0$. This simplifies to $-96 + 24x = 0$. Solving for $x$ yields $24x = 96$, and thus $x = 4$.