Question

Solve:
$\left[\begin{array}{ccc}2& -1& 4\\ 4& -3& 1\\ 1& 2& 1\end{array}\right]$

Answer 1

We have

$\left[\begin{array}{ccc}2& -1& 4\\ 4& -3& 1\\ 1& 2& 1\end{array}\right]$

Now

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

Expanding the given determinant by $1st$ row, we get

$\begin{array}{c}\Delta =2\left|\begin{array}{cc}-3& 1\\ 2& 1\end{array}\right|+1\left|\begin{array}{cc}4& 1\\ 1& 1\end{array}\right|+4\left|\begin{array}{cc}4& -3\\ 1& 2\end{array}\right|\\ =2(-3-2)+1(4-1)+(8+3)\\ =-10+3+44\\ \Delta =37\end{array}$