A Geometric Project for a Linear Algebra Class. Issue 6 (3rd July 2022)

• Record Type: Journal Article
• Authors: Andriunas, R.; Boyle, B.; Lazowski, A.
• Is Part Of: PRIMUS. Volume 32:Issue 6(2022)
• Page Start: 676
• Page End: 684
• Publication Date: 2022-07-03
• Subjects: Linear algebra -- diagonalization -- eigenvectors -- eigenvalues -- geometry -- tetrahedron -- centroid; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2021.1900477
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract : This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and apply eigenvectors, eigenvalues, and diagonalization to calculate a limit. Other concepts found within the project apply cross products and normal vectors. We describe the project's background, offer comments and variations for the given questions, and supply results from administering it ourselves.