The solution to a system of equations goes back to ancient Chinese mathematicsa 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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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

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Here are the Insights into Mathematics Playlists:

   • MathHistory: A course in the History ...  
   • WildTrig: Intro to Rational Trigonometry  
   • Math Foundations  
   • Wild Linear Algebra  
   • Famous Math Problems  
   • Box Arithmetic  
   • Elementary Mathematics (K6) Explained  
   • Year9Maths  
   • Ancient Mathematics  
   • Wild West Banking  
   • Sociology and Pure Mathematics  
   • Sociology and Pure Physics  
   • Old Babylonian Mathematics  
   • Probability and Statistics: an introd...  
   • Boole's Logic and Circuit Analysis  
   • Universal Hyperbolic Geometry  
   • Differential Geometry  
   • Algebraic Topology  
   • MathSeminars  
   • Playing Go  
   • Diffusion Symmetry: A bridge between ...  

Here are the Wild Egg Maths Playlists (some available only to Members!)

   • Algebraic Calculus One  
   • Classical to Quantum  
   • Algebraic Calculus Two  
   • Advice for mathematics exploration  
   • Solving Polynomial Equations | Explor...  
   • The Hexagrammum Mysticum (Members only)  
   • Algebraic Calculus and dCB curves | E...  
   • Dynamics on Graphs  
   • Playlist  
   • Triangle Geometry  
   • Explorations with qseries  
   • Six: An elementary course in Pure Mat...  
   • Maxel Inverses and Orthogonal Polynom...  
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