We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.

We present a short-term class project used in an introductory linear algebra course, designed to engage students in matrix algebra. In this activity, students responded to a survey of their pop culture tastes. Using the survey responses, they worked to design a series of matching algorithms, using matrices, with the goal of matching the students…

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

To teach the rigorous skills and knowledge students need to succeed in future college-entry courses and workforce training programs, education stakeholders have increasingly called for more rigorous curricula, instruction, and assessments. Identifying the critical attributes of rigor and measuring its appearance in curricular materials is…

In this note the well-known Lagrange identity is extended to matrices. The resulting generalized Lagrange identity is used to give characterizations of symmetry, commutativity of projectors and normality.

Two methods for solving matrix equations are discussed. Both operate entirely on a matrix level. (MNS)

Examples for determining the equation of a line through two points or a quadratic function that contains three noncollinear points are presented. (MNS)

Presents a method for using matrix algebra and computers to encode and decode secret messages. Provides examples of coding procedures, a short review of matrix multiplication, and a BASIC program for use with secret messages containing up to 1000 numbers. (RT)

This unit on coding discusses such topics as redundancy, hamming distance, linear codes, and the location of errors. Extensive use is made of matrices and binary numbers. (MP)

Described are procedures for multiplying matrices using Logo. Examples of computer programming are included. (RH)

Provides a program listing in True BASIC which constructs several kinds of matrices: (1) matrices with integral entries that have inverses that have integral entries; (2) matrices with integral entries that have inverses that are rational numbers with reasonable denominators; and (3) matrices with integral entries and prescribed integer…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…