History of the Elimination Methods for Solving Linear Equations
Overview
This paper traces the historical development of elimination methods for solving linear equations from ancient China through the modern era. The author examines contributions by various mathematicians including early Chinese scholars, Isaac Newton, Seki Kowa, Gabriel Cramer, Leonhard Euler, and Carl Friedrich Gauss, arguing that the Gaussian elimination method represents the culmination of centuries of mathematical innovation.
What this essay covers
- Ancient Chinese origins of solving linear equations using counting rods (200 BC)
- European developments from the 1600s-1700s including Newton's manuscripts and Seki Kowa's determinant methods
- Gabriel Cramer's determinant rule and Euler's observations on linear dependence
- Carl Gauss's elimination method and analysis of solution uniqueness
Preview
Student’s Name:
Instructor:
Date:
History of the Elimination Methods for Solving Linear Equations
Math is great. It is a subject you cannot hate because everything revolves around numbers. Real-life situations require you to approximate, integrate, differential, and calculate to find solutions. In my early life as a mathematician, I worked with several individuals in maths and science, including Carl Friedrich Gauss. I was surprised to learn that the algorithm of simultaneously solving linear equation systems is attributed to Gauss.
Different methods for solving simultaneous linear equations existed even before our era and preceded Gauss by more than 2000 years. This idea originated in ancient China in 200BC. Early Chinese mathematicians used counting rods to represent numbers. Elaborate calculations were organized by placing these rods within squares arranged in a rectangle. Each column of squares correlates with a modern linear equation. The counting rods represented problem constraints and were used to specify the sequence of manipulations to be done to solve a particular problem.
The Chinese development may have been lost due to a tradition of impartiality in the primary text. Notable improvements towards finding a comprehensive theory of developing linear equations and their solutions were made between the 1600s and 1700s. The European origin can be traced through its appearance in relatively few significant documents dating back to about four hundred years ago. These include Isaac Newton's manuscripts in the late 1600s. Seki Kowa, a Japanese Mathematician, also came up with a version of determinants to solve nonlinear equations.