English

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

R2 v1 2026-06-28T18:17:15.309Z