Write the value of the determinant
Question:

Write the value of the determinant $\left[\begin{array}{ccc}2 & 3 & 4 \\ 2 x & 3 x & 4 x \\ 5 & 6 & 8\end{array}\right]$.

Solution:

Let $\Delta=\mid \begin{array}{lll}2 & 3 & 4\end{array}$

$\begin{array}{ccc}2 x & 3 x & 4 x \\ 5 & 6 & 8\end{array}$

$=x \mid 2 \quad 3 \quad 4$

$\begin{array}{lll}2 & 3 & 4 \\ 5 & 6 & 8\end{array}$        $\left[\right.$ Taking out $x$ common from $\left.R_{2}\right]$

$=0$