Let \(\Delta=\left|\begin{array}{ccc}243 & 156 & 300 \\ 81 & 52 & 100 \\ -3 & 0 & 4\end{array}\right|\)
Using the property that if the equimultiples of corresponding elements of other rows (or columns) are added to every element of any row (or column) of a determinant, then the value of determinant remains the same
Using row transformation, \(R_{1} \rightarrow R_{1}-3 R_{2}\)
$$
\begin{aligned}
&\text { We get, } \Delta=\left|\begin{array}{ccc}
243-81 \times 3156-52 \times 3300-100 \times 3 \\
81 & 52 & 100 \\
-3 & 0 & 4
\end{array}\right| \\
&=\left|\begin{array}{ccc}
0 & 0 & 0 \\
81 & 52 & 100 \\
-3 & 0 & 4
\end{array}\right|
\end{aligned}
$$
Using the property that if all elements of a row or column of a determinant are 0 , the value of determinant is 0 .
Hence \(\Delta=0\)
