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