Question:
Find the value of the determinant $\left|\begin{array}{ccc}243 & 156 & 300 \\ 81 & 52 & 100 \\ -3 & 0 & 4\end{array}\right|$.
Solution:
$\begin{array}{ccc}\mid 243 & 156 & 300 \\ 81 & 52 & 100 \\ -3 & 0 & 4 \mid\end{array}$
$=\mid 243-(81 \times 3) 156-(52 \times 3) 300-(100 \times 3) 81$ $\begin{array}{llll}52 & 100-3 & 0 & 4 \mid\end{array}$
$\left[\right.$ Applying $\left.R_{1} \rightarrow R_{1}-3 R_{2}\right]$
$=\mid \begin{array}{lll}0 & 0 & 0\end{array}$
$\begin{array}{lll}81 & 52 & 100\end{array}$
$\begin{array}{lll}-3 & 0 & 4 \mid\end{array}$
$=0$