Question

Evaluate \[\begin{vmatrix}4785 & 4787 \\ 4789 & 4791\end{vmatrix}\]

Answer 1

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