The solution to a system of equations goes back to ancient Chinese mathematics–a treatise called the Nine Chapters of the Mathematical Arts. In this video we discuss the further history of this problem and the natural connection with the theory of determinants.

Major contributors include Leibniz, Cramer, Laplace, Vandermonde, Cauchy, Cayley and Sylvester. In particular we look at Cramer’s Rule, Laplace’s expansion of determinants, resultants as described by Euler and Bezout, and then Sylvester’s reformulation of these polynomials as determinants.

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