Topic: Linear Algebra
Given that the following matrix is singular: $\begin{pmatrix}4&2x&0\\ 4&0&2\\ 12&6&0\end{pmatrix}$ The value of x is:
- A. 2
- B. 3
- C. 1
- D. 0
Answer: C. 1
Explanation: For a matrix to be singular, its determinant must be zero. Let's calculate the determinant of the given 3x3 matrix:
$|A| = 4(0 - 12) - 2x(0 - 24) + 0 = 0$
$-48 + 48x = 0$
$48x = 48 \Rightarrow x = 1$.