introduction to linear equations

In mathemathics, a system of linear equations (or linear system) is a collection of linear ecuations involving the same set of variables For example,



is a system of three equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by


since it makes all three equations valid

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 prominent role in ,physics, chemistry, computer ciencie and economics. A system of non-linear equations can often be aproximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.










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