Systems Of Linear Equations

In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a proeminent role in engineering, physics, chemistry, computer science and economics. A system of non-linear equations can often be approximated by a linear system, a helpful technique when making a mathematical model or computer simulation of a relatively complex system. When considering methods for solving systems of linear equations, it is important to distinguish between large systems that must be solved by computer (using programs such as: Mathematica, Maple and Derive) and small systems that can be solved by hand. Some practical applications of solutions of systems of linear equations are: GPS (Global Positioning System), network analysis of traffic flow, electrical circuits and chemical reactions. GPS is the system used by the military, ships, airplane pilots, surveyors, utility companies, automobiles and hikers to locate current positions by communicating with a system of satellites. The concept of network appears in a variety of applications. Loosely stated, a network is a set of branches through which something "flows". For example, the branches might be electrical wires through which electricity flows, pipes through which water or oil flows, traffic lanes through which vehicular traffic flows, or economic linkages through which money flows.