Question

Find the determinant $\left|\begin{array}{ccc}3& 2& 6\\ 1& 1& 2\\ 2& 2& 5\end{array}\right|$

Answer 1

$\begin{array}{c}\Delta =\left|\begin{array}{ccc}3& 2& 6\\ 1& 1& 2\\ 2& 2& 5\end{array}\right|\\ \Delta =3\left|\begin{array}{cc}1& 2\\ 2& 5\end{array}\right|-2\left|\begin{array}{cc}1& 2\\ 2& 5\end{array}\right|+6\left|\begin{array}{cc}1& 1\\ 2& 2\end{array}\right|\\ \Delta =3\left(5-4\right)-2\left(5-4\right)+6\left(2-2\right)\\ \Delta =3-2+0\\ \Delta =1\\ Hence,\\ \Delta =1\end{array}$