A combinatorial proof of Cramer's Rule
By Doron Zeilberger
.pdf
.tex
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org
Written: Aug. 18, 2024
In honor of my Rutgers colleague, Antoni A. Kosinski (b. 1930), who proved that Cramer's Rule is indeed due to Cramer.
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.
Added Aug. 21, 2024: Thanks to Alex Heaton for correcting typos in the previous version.
Maple package
-
Cramer.txt,
a Maple package that confirms Cramer's rule and our combinatorial proof
Personal Journal of Shalosh B. Ekhad and Zeilberger