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Question
If the matrix \[\begin{bmatrix}5x & 2 \\ - 10 & 1\end{bmatrix}\] is singular, find the value of x.
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Solution
A matrix is said to be singular if its determinant is zero. Since the given matrix is singular, we get
\[A = \begin{bmatrix} 5x & 2 \\- 10 & 1 \end{bmatrix} \]
\[ \Rightarrow \left| A \right| = \begin{vmatrix} 5x & 2 \\- 10 & 1 \end{vmatrix} = 0\]
\[ \Rightarrow 5x + 20 = 0 \left[\text{ Expanding }\right]\]
\[ \Rightarrow x = - \frac{20}{5} = - 4\]
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