Linear Systems and Matrices
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This page first made public: Apr 1, 2008
This material is replicated on a number of sites as part of the SERC Pedagogic Service Project
Summary
After covering the standard course material on linear systems and matrices, Linear Algebra students are given a computer-based activity that helps them to develop a better understanding of matrix algebra and connections between linear systems and matrices. Students have their choice of a computer algebra system (CAS) or Internet-based interactive tools from the MERLOT collection referred by the instructor.
Learning Goals
To enable students to:
- develop their understanding of connections between linear systems and matrices
- gain an understanding of basic matrix algebra operations
- apply their knowledge and understanding in solving individualized applied linear algebra problems
- better familiarize themselves with linear algebra tools provided by modern computer algebra systems
Context for Use
This activity is designed for a Linear Algebra class and gives an opportunity for students to exercise their analytical and computer skills with regard to applied problems of linear algebra and matrix analysis. The main part of the activity takes the form of a take-home project that is numerically individualized using students' ID information.
The activity requires approximately 2 hours to complete
The activity requires approximately 2 hours to complete
Description and Teaching Materials
Activity description:
- Students are given a Project Worksheet (Acrobat (PDF) 66kB Feb4 08)
containing 10 application-based linear algebra problems. Each problem is based on the numeric info related to a part of student's ID information. All of the problems are based on the material taught during a standard course of Linear Algebra and require mostly basic knowledge of matrix operations.
- The instructor gives students a choice of available CAS (computer algebra system) and gives an introductory lecture on required syntax and user interface commands. The students, however, should be able to use the computer algebra systems that they prefer.
- Afterwards, the instructor presents interactive Java applets that can be used instead of or in addition to the computer algebra systems. The choice of two or three different applets should be sufficient for the activity completion.
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Matrix Multiplier
This site contains a tool that allows a user to rapidly compute the product (or other operation) of two matrices. MERLOT description of this resource
Matrix calculator
Matrix Calculator is a site containing an interactive applet that allows a user to input a square matrix and then, with a press of a button, compute a power of this matrix, determinant, inverse, characteristic polynomial and other useful matrix characteristics. MERLOT description of this resource
Linear System Solver
This site contains a Java applet that allows the user to solve a system of three linear equations involving three variables. The applet also calculates the determinant of a coefficient matrix. MERLOT description of this resource
Teaching Notes and Tips
This activity leads students to develop a better and deeper understanding of applied problems that Linear Algebra and Matrix Analysis are dealing with.
An individualized format of this activity makes the instructor sure that at least a majority of the work was performed by a particular student.
Several questions in this project should lead students toward a discussion that should help in understanding the basic concepts of Linear Algebra.
An individualized format of this activity makes the instructor sure that at least a majority of the work was performed by a particular student.
Several questions in this project should lead students toward a discussion that should help in understanding the basic concepts of Linear Algebra.
Assessment
Assessment is optional; the intent is to develop students' understanding of matrix algebra and analysis.
References and Resources
MIT OpenCourseWare: Linear Algebra Video Lectures
This site provides a series of Professor Strang's Linear Algebra Lecture Videos. MERLOT description of this resource
This site provides a series of Professor Strang's Linear Algebra Lecture Videos. MERLOT description of this resource