Determinants

Solution We have \(|\begin{smallmatrix}3&x\\ x&1\end{smallmatrix}|=|\begin{smallmatrix}3&2\\ 4&1\end{smallmatrix}|\) i.e. \(3-x^{2}=3-8\) i.e. \(x^{2}=8\) Hence \(x=\pm2\sqrt{2}\)