Show that, for all $\rho > 0$ and all $m , n \in \mathbb { N } ^ { * }$, the sets $\mathscr { D } _ { \rho } ( \mathbb { R } ) , \mathscr { D } _ { \rho } \left( \mathbb { R } _ { n } [ X ] \right)$ and $\mathscr { D } _ { \rho } \left( \mathscr { M } _ { m , n } ( \mathbb { R } ) \right)$ are closed under addition.