\(\begin{vmatrix} 3 & 1 & 2 \\ -1 & 4 & 1 \\ 2 & 1 & 3 \end{vmatrix} = 3\begin{vmatrix} 4 & 1 \\ 1 & 3 \end{vmatrix} - 1\begin{vmatrix} -1 & 1 \\ 2 & 3 \end{vmatrix} + 2\begin{vmatrix} -1 & 4 \\ 2 & 1 \end{vmatrix}\) = 3(12 - 1) - 1(-3 - 2) + 2(-1 - 8) = 3(11) - 1(-5) + 2(-9) = 33 + 5 - 18 = 20.