ABSTRACT
This chapter discusses the approaches that can be used to solve a linear system of equations. It explores matrix formalities, condition number, error effects, and solution techniques for linear systems. The systems, whether linear or nonlinear, require the inversion of a matrix set for calculating the physical variables of the problem. Linear matrices result from those physical systems that obey laws that are path independent. Path-dependent systems require the careful documentation of each step in the solution process, the final result depends on the manner in which that solution was attained. The discussion of a matrix condition begins with the definition of a quantity called a condition number. The discussion of direct matrix solution methods ends with the introduction of an important technique that is used in many practical applications. In normal matrix operations, the known values of the x vector would be subtracted from the set of simultaneous equations and the size of the matrix system would be reduced.
