Question

If $A=\left[\begin{array}{ccc}1& 0& 0\\ 2& 3& 4\\ 5& -6& x\end{array}\right]$ and $detA=45$; then find $x$.

Answer 1

$\text{det(A)}=\left|\begin{array}{ccc}1& 0& 0\\ 2& 3& 4\\ 5& -6& x\end{array}\right|=1(3x+24)$, expand along first row

$\Rightarrow 45=3x+24$

$\Rightarrow 3x=45-24=21$

$\therefore x=7$