For what value of x is the matrix 6-x&4 3-x&1 singular? - Vidyadip

Question

For what value of x is the matrix $\begin{bmatrix}6-\text{x}&4\\3-\text{x}&1\end{bmatrix}$ singular?

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Answer

$\begin{bmatrix}6-\text{x}&4\\3-\text{x}&1\end{bmatrix}$ is singular when its determinant is 0.
$\Rightarrow\begin{bmatrix}6-\text{x}&4\\3-\text{x}&1\end{bmatrix}=0$
$\Rightarrow(6-\text{x})-4(3-\text{x})=0$
$\Rightarrow6-\text{x}-12+4\text{x}=0$
$\Rightarrow3\text{x}-6=0$
$\Rightarrow3\text{x}=6$
$\Rightarrow\text{x}=\frac{6}{2}$
$\Rightarrow\text{x}=2$

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