Abstract:

Concepts of transition matrix and matrix transformation often cause confusion among the students of an introductory linear algebra course. Those two expressions sound similar but have very different meanings and applications. To make things even more challenging, both of these concepts are often simultaneously used in a solution process of some common problems pertaining to linear algebra. To help distinguish between them, the authors propose the use of Microsoft Excel as an instructional tool assisting engineering students in the mastery of these mathematical concepts. An integral component of such a project is the exploration of an interactive spreadsheet. To grasp the concept of transition matrix, students are invited to select from a list of preprogramed bases presented in a form of a dropdown menu. The effect of the action of a transition matrix will be illustrated in a form of changing coordinates for a given input point. Moreover, a choice of classic matrix transformations will be offered from a list presented in a form of a dropdown menu. Students can then visualize the impact of the action of a chosen matrix transformation on an input vector and witness its transformation on a graph. Further, students could also create their own transition matrix or matrix transformation by providing expressions of their own choice. Authors hence propose an effective use of Excel to help students gain an insight into the behavior of and difference between a transition matrix and a matrix transformation. This approach promotes students’ interest in and mastery of these important mathematical concepts and further improves students’ mathematical skills.

Keywords:

Transition matrix, matrix transformation, change of basis, engineering education.