Introduction to Applied Algebra: Book Review of Chapter 8-Linear Equations (System of Linear Equations)

Abstract

This chapter review presents two ideas and techniques in solving Systems of Linear Equations in the most simple minded straightforward manner to enable the student as well as the instructor to follow it independently with very little guidance. The focus is on using simpler and easier approaches such as Determinants; and Elementary Row Operations to solve Systems of Linear Equations. We found the solution set of a few systems of linear equations by a successive ratio of the determinant of all the matrices formed from replacing each column of the coefficient matrix by the right hand side vector and the determinant of the coefficient matrix repeatedly giving the values of the variables in the system in the order in which they appeared. Similarly, we also used the three types of elementary row operations namely; Row Swap; Scalar Multiplication; and Row Sum to find the solution set of systems of linear equations through row echelon form to reduced row echelon form to find the solution set of some systems of linear equations. Technical forms of systems of linear equations were used to illustrate the two approaches in finding their solution sets. In each approach we started by finding the coefficient matrices from the systems of linear equations.