DETERMINANTS AND MATRICES

In many areas of mathematical analysis, we encounter systems of ordered sets of elements, which could be sets of numbers, functions, or even equations. In this chapter, the authors present a formal treatment of matrices and determinants and their applications to systems of linear equations. They introduce determinants that play a very important role in the theory of matrices. Determinants are scalars associated with square matrices. Evaluation of determinants by using the basic definition is practical only for small orders, usually up to 3 or 4. If two rows or columns of a square matrix are proportional, then its determinant is zero. If two rows or columns of a determinant are interchanged, then the value of…