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Question
Write the value of the determinant \[\begin{vmatrix}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x\end{vmatrix}\]
Sum
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Solution
\[\begin{vmatrix}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x\end{vmatrix}\]
\[ = \begin{vmatrix}2 & 3 & 4 \\ 5 & 6 & 8 \\ 2 & 3 & 4\end{vmatrix} \left[\text{ Taking 3x common from }R_3 \right]\]
\[ = 0 \left[ \because R_1\text{ and }R_3\text{ are identical }\right]\]
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