Write the value of the determinant
Question:

Write the value of the determinant $\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$

Solution:

$\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$

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

$=0$    $\left[\because R_{1}\right.$ and $R_{3}$ are identical $]$

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