PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Solving linear systems: Augmented matrices and the reconstruction of x
Page: 1072
The origins of linear algebra lie in efforts to solve systems of linear equations and understand the nature of their solution sets. In our experience, instructors of linear algebra see the work of teaching students to solve linear systems as the more straightforward and procedural portion of the course. We speculate that solving linear systems and interpreting their solution sets in fact entails hidden and significant challenges for students that are important for their later success in linear algebra, as well as their work in related STEM courses. In this paper, we examine final exam data from 69 students in an introductory undergraduate linear algebra course at a large public university in the southwestern US. Our analysis suggests that students are largely successful in representing systems of linear equations using augmented matrices, but that interpreting the row reduced echelon form of these matrices is a common source of difficulty.