There are many situations in pure and applied mathematics, theory of electrical circuits, aerodynamics, nuclear physics, and astronomy in which we have to deal with algebraic structures and rectangular array of numbers or functions. These arrays will be called matrices. The aim of this chapter is to study algebraic structures and algebra of matrices along with its application to the study of system of linear equations.
13.1 CONCEPTS OF GROUP, RING, AND FIELD
Definition 13.1. Let S be a non-empty set. Then a mapping f : S × S → S is called a binary operation in S.
A non-empty set along with one or more binary operations defined on it is called an algebraic structure.
Definition 13.2. A non-empty set G together with a binary ...
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