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Question
For what value of x is the matrix \[\begin{bmatrix}6 - x & 4 \\ 3 - x & 1\end{bmatrix}\] singular?
Solution
\[\begin{vmatrix}6 - x & 4 \\ 3 - x & 1\end{vmatrix}\text{ is singular when its determinant is 0 .} \]
\[ \Rightarrow \begin{vmatrix}6 - x & 4 \\ 3 - x & 1\end{vmatrix} = 0\]
\[ \Rightarrow \left( 6 - x \right) - 4\left( 3 - x \right) = 0\]
\[ \Rightarrow 6 - x - 12 + 4x = 0\]
\[ \Rightarrow 3x - 6 = 0\]
\[ \Rightarrow 3x = 6\]
\[ \Rightarrow x = \frac{6}{3} = 2\]
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