Question

The value of the determinant $\Delta =\left|\begin{array}{ccc}5& 23& 12\\ 10& 36& 24\\ 15& 63& 36\end{array}\right|$ is

Answer 1

Given, $\Delta =\left|\begin{array}{ccc}5& 23& 12\\ 10& 36& 24\\ 15& 63& 36\end{array}\right|$
Take $\left(5\right)$ common from $C_1$ and $\left(12\right)$ common from $C_3$, we get
$\Delta =5\cdot 12\left|\begin{array}{ccc}1& 23& 1\\ 2& 36& 2\\ 3& 63& 3\end{array}\right|$
$\Rightarrow \Delta =0$
$(\because C_1$ and $C_3$ are identical)