Let $\Lambda\subseteq R^n$ contains $m$ elements, where $\lambda_i$ is the $ith$ element, and $co(\Lambda)$ is the smallest convex cone contains $\Lambda$. Also, consider any point $u\in R^n$. Now, I would like to prove that $u\in co(\Lambda)$ if and only if $\Lambda^* \subseteq \{u\}^*$.
I think it is a well-known theorem, but I don't know its name; and so, I can't find it in the literature. The proof from left to right is pretty straightforward and I can do, but I can't figure out how to obtain the left side from the right.