Question

Solve:
$\left[\begin{array}{ccc}1& 4& 2\\ 2& -1& 4\\ -3& 7& 6\end{array}\right]$

Answer 1

we have

$\left[\begin{array}{ccc}1& 4& 2\\ 2& -1& 4\\ -3& 7& 6\end{array}\right]$

now

$\Delta =\left|\begin{array}{ccc}1& 4& 2\\ 2& -1& 4\\ -3& 7& 6\end{array}\right|$

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

$\begin{array}{c}\Delta =1\left|\begin{array}{cc}-1& 4\\ 7& 6\end{array}\right|-4\left|\begin{array}{cc}2& 4\\ -3& 6\end{array}\right|+\left|\begin{array}{cc}2& -1\\ -3& 7\end{array}\right|\\ =1(-6-28)-4(12+12)+2(14-3)\\ =-34-96+22\\ =-130+22\\ =-108\end{array}$

Hence,

$\Delta =-108$