Question

The value of $\Delta =\left|\begin{array}{ccc}1& 2& 4\\ -1& 3& 0\\ 4& 1& 0\end{array}\right|$ is

Answer 1

Note that in the third column,two entries are zero, So expanding along third column $(C_3,)$ we get

$\Delta =4\left|\begin{array}{cc}-1& 3\\ 4& 1\end{array}\right|-0\left|\begin{array}{cc}1& 2\\ 4& 1\end{array}\right|+0\left|\begin{array}{cc}1& 2\\ -1& 3\end{array}\right|$

$=4(-1-12)-0+0=-52$