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Question
Evaluate \[\begin{vmatrix}4785 & 4787 \\ 4789 & 4791\end{vmatrix}\]
Solution
\[\text{ Let }\Delta = \begin{vmatrix}4785 & 4787 \\ 4789 & 4791\end{vmatrix}\]
\[ \Rightarrow \Delta = \begin{vmatrix}4785 & 2\\ 4789 & 2\end{vmatrix} \left[\text{ Applying }C_2 \to C_2 - C_1 \right]\]
\[ = 2 \times \begin{vmatrix}4785 & 1\\ 4789 & 1\end{vmatrix}\]
\[ = 2 \times \left( 4785 - 4789 \right) = 2 \times \left( - 4 \right) = - 8\]
\[ \Rightarrow \begin{vmatrix}4785 & 4787 \\ 4789 & 4791\end{vmatrix} = - 8\]
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