Pedagogy of Solutions to a Set of Linear Equations Using a Matlab Workbook

摘要

A Matlab workbook capable of generating complete solutions to a set of linear equations is presented. While standard routines in Matlab and Maple provide solutions to a set of equations, additional work is needed to interpret and relate them to the concepts covered in an undergraduate course in Linear Algebra. One also runs into difficulties when the system of equations is inconsistent. The workbook, started as a simple demo for students, evolved into its present form where the solutions to a set of linear equations are displayed on a single page with explanations, annotations, and equations that match the work by the instructor in class. Regardless of whether the system is consistent or inconsistent with general or unique solutions, the solution set is presented with information such as the rank of a matrix, pivots, null space, free and basic variables, etc., providing the pedagogy. The solutions are compared to those obtained using standard packages from Matlab and Maple demonstrating their shortcomings and limits. In contrast, the results of the workbook provide complete instructive aspects of solutions to a set of linear equations enhancing the educational experience of students. (c) 2017 Wiley Periodicals, Inc.