Question

Find the value of the determinant $\left|\begin{array}{ccc}243& 156& 300\\ 81& 52& 100\\ -3& 0& 4\end{array}\right|.$

Answer 1

$$\begin{gathered} \left|243156300 \\ 8152100 \\ -304\right| \\ =\left|243-\left(81\times 3\right)156-\left(52\times 3\right)300-\left(100\times 3\right) \\ 8152100 \\ -304\right|\left[\mathrm{Applying}{R}_1\to R_1-3R_2\right] \\ =\left|000 \\ 8152100 \\ -304\right| \\ =0 \end{gathered}$$