Simultaneous Linear Equations

Abstract

Linear algebra is introduced using simultaneous equations. Linear transformations are used to introduce the idea of vectors and matrices. The concept of a finite dimensional linear vector space is introduced for describing the properties of vectors. Basis vectors and rules for vector addition and scalar products are defined. Linear transformation are interpreted as the action of matrices on vectors and which yields the defining equations of how vectors are transformed under the action of matrices. The generalization of vectors to N-dimensions is made.