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  4. For what value of x, matrix [ beginmatrix6-x&4 3-x&1 endmatrix] is a singular matrix?

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Q. For what value of $x$, matrix $\left[\begin{matrix}6-x&4\\ 3-x&1\end{matrix}\right]$ is a singular matrix?

Determinants

Solution:

Matrix $A$ is singular, when $|A| = 0$
$\left|\begin{matrix}6-x&4\\ 3-x&1\end{matrix}\right|=0$
$\Rightarrow \quad6-x-12+4x=0 \Rightarrow \,3x=6\, \Rightarrow \, x=2$