A combinatorial proof of Cramer's Rule
Combinatorics
2024-08-26 v2
Abstract
In 1750, Gabriel Cramer famously stated, without proof, his eponymous rule for solving a system of linear equations with as many equations as unknowns. We give a purely combinatorial, and purely self-contained, proof of this old chestnut, still useful after all these years.
Cite
@article{arxiv.2408.10282,
title = {A combinatorial proof of Cramer's Rule},
author = {Doron Zeilberger},
journal= {arXiv preprint arXiv:2408.10282},
year = {2024}
}
Comments
4 pages. This version corrects typos kindly pointed out by Alex Heaton