Matrix Methods of Linear Algebra

or

Curriculum Module

Created with R2024a. Compatible with R2024a and later releases.

Information

This curriculum module contains interactive MATLAB® live scripts that teach fundamental matrix methods commonly taught in introductory linear algebra courses. In the first part of each live script, students learn standard definitions, visualize concepts, and perform exercises on paper. Afterward, students practice complementary MATLAB® methods. These methods reinforce the discussed concepts and help students to develop an early familiarity with computational software. Each lesson concludes with an illustrative application.

Background

You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. This module covers topics such as matrix operations, linear systems, determinants, eigenvalues and eigenvectors, and diagonalization. It also includes examples of using matrix methods to modify grayscale images, analyze linear circuits, understanding vibrations, and Markov chains.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Contact Us

Solutions are available upon instructor request. Contact the MathWorks teaching resources team if you would like to request solutions, provide feedback, or if you have a question.

Getting Started

Accessing the Module

On MATLAB Online:

Use the link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.

On Desktop:

Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double-click on MatrixMethods.prj. It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.

Ensure you have all the required products (listed below) installed. If you need to include a product, add it using the Add-On Explorer. To install an add-on, go to the Home tab and select Add-Ons > Get Add-Ons.

Products

MATLAB® is used throughout. Tools from Symbolic Math Toolbox™, Statistics and Machine Learning Toolbox™, and Image Processing Toolbox™ are used as well.

Scripts

MatrixOperations.mlx

	In this script, students will... $\bullet$ Define matrices and their basic arithmetic operations $\bullet$ Calculate the result of matrix operations on paper and in MATLAB $\bullet$ Explain the size requirements of matrix operations $\bullet$ Compare symbolic and numeric matrix operations in MATLAB $\bullet$ Apply matrix methods to modify grayscale images	Academic disciplines $\bullet$ Linear algebra $\bullet$ Image processing

LinearSystems.mlx

	In this script, students will... $\bullet$ Write a linear system in matrix form $\bullet$ Relate solutions of linear systems in 3-dimensions to their visualizations $\bullet$ Solve systems of linear equations using row-reduction and matrix inverses $\bullet$ Explain the solvability of a linear system in terms of the matrix determinant $\bullet$ Use MATLAB to solve linear systems	Academic disciplines $\bullet$ Linear algebra

LinearSystemsApplications.mlx

	In this script, students will... $\bullet$ Apply matrix methods to linear regression and linear circuit analysis	Academic disciplines $\bullet$ Linear algebra $\bullet$ Statistical analysis $\bullet$ Circuit analysis

Eigenanalysis.mlx

	In this script, students will... $\bullet$ Visualize eigenvectors in 2-dimensions $\bullet$ Solve for the eigenvalues and eigenvectors of a 2x2 matrix on paper and larger matrices using MATLAB $\bullet$ Diagonalize 2x2 matrices on paper and larger matrices in MATLAB $\bullet$ Explain linear system solvability in terms of eigenvalues $\bullet$ Discuss defective matrices	Academic disciplines $\bullet$ Linear algebra

EigenanalysisApplications.mlx

	In this script, students will... $\bullet$ Use eigenanalysis to understand vibrations and the long term behavior of a Markov chain	Academic disciplines $\bullet$ Linear algebra $\bullet$ Physical systems $\bullet$ Statistical modeling

Related Courseware Modules

Vector Arithmetic

	Available on: GitHub

Applied Linear Algebra

	Available on: GitHub

Or feel free to explore our other modular courseware content.

Educator Resources

• Educator Page

Contribute

Looking for more? Find an issue? Have a suggestion? Please contact the MathWorks teaching resources team. If you want to contribute directly to this project, you can find information about how to do so in the CONTRIBUTING.md page on GitHub.

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