Let $\mathcal { W }$ be a vector subspace of $\mathcal { M } _ { n , 1 } ( \mathbb { R } )$ of dimension $d$. Prove that $$\operatorname { card } \left( \mathcal { W } \cap \mathcal { V } _ { n , 1 } \right) \leqslant 2 ^ { d }$$
Let $\mathcal { W }$ be a vector subspace of $\mathcal { M } _ { n , 1 } ( \mathbb { R } )$ of dimension $d$. Prove that
$$\operatorname { card } \left( \mathcal { W } \cap \mathcal { V } _ { n , 1 } \right) \leqslant 2 ^ { d }$$