Linear algebra and the HP49G - A partnership for less tedium and more understanding

Abstract

Milton Fuller Mathematics Learning Centre Central Queensland University Rockhampton, Queensland Australia Abstract Linear algebra has always been an important part of undergraduate mathematics. However, with the emergence of sciences such as signal processing and computer graphics, linear algebra is currently "enjoying a renaissance" as an essential component of applied mathematics. William McWhorter and Leroy Meyers in a paper on computing eigenvalues and eigenvectors without determinants in the February edition of Mathematics Magazine wrote "who … would demand that a student use a determinant to compute by hand the eigenvalues and eigenvectors of the matrix A" (A is a square matrix of order 4). The authors then demonstrate a faster method for finding the eigenvalues and eigenvectors of A, "in a few minutes on less than half a sheet of paper". The aim of this paper is to demonstrate the features of the Hewlett Packard HP49G graphics calculator. The emphasis will be on illustrating the power of this hand held technology to carry out, without resort to pencil and paper: § Matrix operations. § Matrix inversion and the solution of sets of linear equations. § The calculation of eigenvalues and eigenvectors. § Diagonalisation of matrices § Applications of powers of matrices.