Question

Evaluate the determinant $\Delta =\left|\begin{array}{ccc}1& 2& 4\\ -1& 3& 0\\ 4& 1& 0\end{array}\right|$

Answer 1

$\Delta =\left|\begin{array}{ccc}1& 2& 4\\ -1& 3& 0\\ 4& 1& 0\end{array}\right|$
$=1\left|\begin{array}{cc}3& 0\\ 1& 0\end{array}\right|-2\left|\begin{array}{cc}-1& 0\\ 4& 0\end{array}\right|+4\left|\begin{array}{cc}-1& 3\\ 4& 1\end{array}\right|$
$=1\left(3\right(0)-1(0\left)\right)-2(-1(0)-4(0)+4(-1\left(1\right)-4\left(3\right))$
$=1\left(0\right)-2\left(0\right)+4(-1-12)$
$=4(-13)$
$=-52$