Let $u = \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}$ and $v = \begin{pmatrix} 1 \\ 4 \\ 2 \end{pmatrix}$ be vectors in $\mathbb{R}^3$. Find the determinant of the matrix $M = 2I_3 + uv^T$.