Linear systems
Linear systems [ edit ] Main article: System of linear equations A finite set of linear equations in a finite set of variables, for example, x 1 , x 2 , ..., x n , or x , y , ..., z is called a system of linear equations or a linear system . [10] [11] [12] [13] [14] Systems of linear equations form a fundamental part of linear algebra. Historically, linear algebra and matrix theory has been developed for solving such systems. In the modern presentation of linear algebra through vector spaces and matrices, many problems may be interpreted in terms of linear systems. For example, let 2 � + � − � = 8 − 3 � − � + 2 � = − 11 − 2 � + � + 2 � = − 3 ( S ) be a linear system. To such a system, one may associate its matrix � = [ 2 1 − 1 − 3 − 1 2 − 2 1 2 ] . and its right member vector � = [ 8 − 11 − 3 ] . Let T be the linear transformation associated to the matrix M . A solution...