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 $\left.R_{2}\right]$
$=0$
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