Question:
Evaluate $\left|\begin{array}{ll}4785 & 4787 \\ 4789 & 4791\end{array}\right|$
Solution:
Let $\Delta=\mid \begin{array}{ll}4785 & 4787\end{array}$
$\begin{array}{ll}4789 & 4791 \mid\end{array}$
$\Rightarrow \Delta=\mid 4785 \quad 2$
$\begin{array}{lll}4789 & 2 & {\left[\text { Applying } C_{2} \rightarrow C_{2}-C_{1}\right]}\end{array}$
$=2 \times \mid 4785 \quad 1$
$\begin{array}{ll}4789 & 1\end{array}$
$=2 \times(4785-4789)=2 \times(-4)=-8$
$\Rightarrow \mid 4785 \quad 4787$
$4789 \quad 4791 \mid=-8$