In many documents about oriented matroids, it is stated as an observation that every rank 2 oriented matroid is realizable. However, I did not find any document where the proof is given.
Do you know any reference where this proof is written?
Thank you!
P.S. This question has already been asked here: every rank 2 oriented matroid is realizable However, the link provided in the answer is not valid anymore
One can find a proof of this result in Section 3.2 of Jürgen Bukowski's Computational Oriented Matroids.