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Question
Write the value of the determinant
\[\begin{bmatrix}2 & 3 & 4 \\ 2x & 3x & 4x \\ 5 & 6 & 8\end{bmatrix} .\]
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Solution
\[Let \Delta = \begin{vmatrix} 2 & 3 & 4\\ 2x & 3x & 4x \\ 5 & 6 & 8 \end{vmatrix}\]
\[ = x\begin{vmatrix} 2 & 3 & 4\\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{vmatrix} \left[\text{ Taking out x common from }R_2 \right]\]
\[ = 0\]
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