Exploring Linear Algebra

Labs and Projects with MATLAB®

Crista Arangala

• Publisher: Chapman and Hall/CRC
• Year: 2019
• Print ISBN: 9781138063518
• eBook ISBN: 9781351664073
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Exploring Linear Algebra: Labs and Projects with MATLAB® is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part, labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections.

The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB® coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way.

Features:

• The book's inquiry-based approach promotes student interaction
• Each chapter contains a project set which consists of application-driven projects emphasizing the chapter's materials
• Adds a project component to any Linear Algebra course
• Explores many applications to a variety of fields that can promote research projects
• Employs MATLAB® to calculate and explore concepts and theories of linear algebra

1

Matrix Operations

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Lab 0: An Introduction to MATLAB®

Introduction

MATLAB is a computer programming language that allows for matrix manipulation. MATLAB only recognizes certain commands that are relative to this program. Therefore you must type the commands as you see them. MATLAB is also case sensitive which means that if you see uppercase you must type uppercase and if you see lowercase you must type lowercase.

There are two ways that you can effectively use a MATLAB command. One way to run a MATLAB command is to type the command directly in the Command Window next to the ≪ symbol and then hit return. This process is convenient when processing only one command at a time makes sense. When you wish to evaluate more than one command at once, it might make more sense to open a MATLAB script.

In order to start a MATLAB script, click on New Script in the tool bar and start typing your commands. In order to process your script after typing it, save your script and then click on the run button in the tool bar. It is also important to note that if you close MATLAB and come back to your work later, your work is not stored in the memory so it is a good idea to save your work so that you can reevaluate it later.

At any point if you are having difficulties, use the Help menu; it is very helpful.

For each lab, you will have to open a new MATLAB script file, also called an Editor file, and type all solutions in this document. So let’s begin there.

Open a new MATLAB script file by choosing the New drop down menu followed by the script choice.

To save this file, choose Save in the drop down menu. Save this file as lab0.m.

Exercises:

a. Type: x=6 and then press the Run button in the tool menu. Notice that the output will show up in the Command window (which is a separate window from the Editor).

b. On the next line in the Editor, type: x=6; and then press the run button. What is the difference between the output in part a and the output here? In each case, MATLAB stores 6 in the variable x.

c. Type: x+5 and then press run.

d. Type: disp(‘x+5’) and on the next line type disp(x+5), then Run. Which x + 5 in the display statement actually produces the value 11?

In order to comment a line out in the editor put a % at the beginning of t...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• 1 Matrix Operations
• 2 Invertibility
• 3 Vector Spaces
• 4 Orthogonality
• 5 Matrix Decomposition with Applications
• 6 Applications to Differential Equations
• MATLAB Demonstrations and References
• Index