Suppose we are given two vectors $b_1, b_2 \in \mathbb{R}^n$ and $m \leq n$ vectors $a_1, \dotsc, a_m \in\mathbb{R}^n$ with
- $ a_1, \dotsc, a_m \notin \text{cone}\, (b_1,b_2) $
- $ \text{cone}(a_1, \dotsc, a_m) \cap \text{cone}\, (b_1,b_2) \neq \emptyset$
Is the following statement true or false?
- $ \text{cone}\, (b_1,b_2) \subseteq \text{cone}(a_1, \dotsc, a_m) $
Thank you very much for your reply.