Question

Find the value of $x$ if $\left|\begin{array}{ccc}3& 5& x\\ 2& 4& 1\\ -1& 2& 3\end{array}\right|=0$

Answer 1

$\left|\begin{array}{ccc}3& 5& x\\ 2& 4& 1\\ -1& 2& 3\end{array}\right|=0$

$\Rightarrow 3(12-2)-5(6+1)+x(4+4)=0$

$\Rightarrow 3\left(10\right)-5\left(7\right)+x\left(8\right)=0$

$\Rightarrow 30-35+8x=0$

$\Rightarrow -5+8x=0$

$\Rightarrow 8x=5$

$\therefore x=\frac{5}{8}$