Evaluate 4785&4787 4789&4791 - Vidyadip

Question

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

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Answer

Let $\triangle=\begin{vmatrix}4785&4787\\4789&4791\end{vmatrix}$
$\Rightarrow\triangle=\begin{vmatrix}4785&2\\4789&2\end{vmatrix}$ [Applying $C_2 \rightarrow C_2 - C_1$]
$=2\times\begin{vmatrix}4785&1\\4789&1\end{vmatrix}$
$=2\times(4785-4789)$
$=2\times(-4)=-8$
$\Rightarrow\begin{vmatrix}4785&4787\\4789&4791\end{vmatrix}=-8$

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