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MATH 22AL: Linear Algebra Computer Laboratory
Ali A. Daddel
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Front Matter
Colophon
Introduction
Course Information
1
LAB 1
Notes
Content and Objectives
Starting Your Work
Entering Vectors
Entering Matrices
Combining Commands
Working with Entries
Diagonal Matrices
Constructing Large Matrices
Creating Vectors (1)
Creating Vectors (2)
Creating Vectors (3)
Row Operations
Saving, Editing and Submitting your work
Historical Notes 1
2
LAB 2
Notes
Content and Objectives
Starting Your Work
Format
Extracting Triangular Matrices
Matrix Operations
Triangular Matrices
Answer the Following Questions
Diagonal Matrices
Symmetric and Skew Symmetric Matrices
Answer the Following Questions (2)
Solve the Linear System
Using MATLAB's Command X=A \ b to Solve a Linear System
Saving, Editing and Submitting your work
Historical Notes 2
3
LAB 3
LAB 3 needs special attention
Notes
Content and Objectives
Starting Your Work
Plotting Graphs
M-Files
Linear Transformations
Matrix Multiplication
Saving, Editing and Submitting your work
Historical Notes 3
4
LAB 4
Notes
Content and Objectives
Starting Your Work
Working with MATLAB
Using Gauss-Jordan Elimination to Calculate
LU Factorization
Saving, Editing and Submitting your work
Historical Notes 4
5
LAB 5
Notes and Objectives
Starting Your Work
Background Linear Combinations
Using MATLAB
Background Linear Combinations (2)
Spanning Set of a Vector Space
MATLAB Exercise
Linearly Independent Vectors
MATLAB Exercise (2)
BASIS and MATLAB Exercise (3)
MATLAB Exercise (4)
Saving, Editing and Submitting your work
Historical Notes 5
6
LAB 6
Notes and Objectives
Starting Your Work
Background Reading and Example
Background Reading: How to Use MATLAB to Study the Row Space of a Matrix A?
Example (2)
Example (3)
Note
Exercise
Null Space
Background Reading: How to Use MATLAB to Find a Basis Null Space of A
Note
Exercise (2)
An Other Way of Finding a Basis for Null-Space of a Matrix
Exercise (3)
Background Reading: Column Space
How to Use MATLAB to Find a Basis for col(A) Consisting of Column Vectors
Exercise (4)
How to Find Basis for Row Space of AB Using Column Space and Independent Columns of Matrix AB
Using M-file to Find a Basis for Null-Space of AB
Saving, Editing and Submitting your work
Historical Notes 6
7
LAB 7
Notes and Objectives
Starting Your Work
Background Reading: Introduction and Origin of Inconsistent Systems
Example
Background Reading: Minimizing Ax-b
Orthogonal Projection of b onto W
Background Reading: Least Square Lines and Example (2)
Example (3)
Exercises: Problem
Exercises: Problem (2)
Exercises: Problem (3)
Exercises: Problem (4)
Saving, Editing and Submitting your work
8
LAB 8
Notes and Objectives
Starting Your Work
Background Reading: Introduction to Determinants
Explore What Happens to the Determinant of a Matrix A when you Perform Row Operation on A
Do the Following Exercises
What Happens to det(D) when a Row of D is Multiplied by a Number (Scalar)?
Do the following exercises (4.3)
Adding a Multiple of the i^th row to the j^ith row
Exercises: Problem
Explore What is the Determinant of FG, and H^n
Explore What is the Determinant of kA
Explore What is the Determinant of AB, and A^-1
Explore Determinant of A+B, and A-B
Explore Determinant of A
Saving, Editing and Submitting your work
9
LAB 9
Notes and Objectives
Starting Your Work
Examples
Examples (2)
Definitions
An Application
How to find Eigenvalues and Eigenvectors Using MATLAB
How to find Eigenvalues and Eigenvectors Using MATLAB (cont.)
Saving, Editing and Submitting your work
10
LAB 10 (Extra Credit)
Notes and Objectives
Starting Your Work
Introduction
Basics of Complex Numbers
Real and Imaginary Part of a Complex Number
Polar Representation of Complex Numbers
Entering Complex Number in MATLAB
Sum, Difference, and Product of Complex Numbers
Conjugate of Complex Number and Division of Complex Numbers
Division of Complex Numbers
Matrices with Complex Entries
Properties of Conjugate of a Matrix
Hermitian Matrix
Normal Matrix
Excercise
Summary: MATLAB and Complex Numbers
Summary: MATLAB and Complex Numbers (cont.)
Exercise (2)
Excercise (3)
Saving, Editing and Submitting your work
11
Historical Notes
Vectors and Matrices
How Matrices are used part 1
How Matrices are used part 2
Ancient time-18th Century
19th Century
20th Century
A Short History of MATLAB
A Short History of Complex numbers
A short history of Matrices and Determinants on MacTutor History of Mathematics Archive
12
Logestics
Due Dates
Grading
How to Access Graded Assignments
Late Enrollment
Frequently asked questions
13
Theoretical and Reading Materilas
Linear Algebra
Fundamental Elments
Matrix Multiplication
Inverse of A matrix
LU Factorization
Linear Combination
Spanning Set
Basis
Row and Column Vectors
Row and Column Space
Null Space
Finding Null Space
Inconsistent System
"Solving" Inconsistant System
Least Square
Orthogonal Projections
Determinants
How to Find Determinants
Eigenvalues Eigenvectors
Eigenvalues Definition
Eigenvalues an application
Complex Numbers History
Complex Numbers
Complex Numbers Polar Representation
Complex Numbers Operations Part 1
Complex Numbers Operations Part 2
Complex Matrices
Conjugate of a Complex Matrices
Hermitian Matrices
Normal Matrices
14
Applications
Least Square approximation
Traffic Flow
Electrical Circuits
Determinant
Genetics
Graph Theory
Cryptography
Markov Chain
Leonteif Economic Model
Authored in PreTeXt
MATH 22AL: Linear Algebra Computer Laboratory
Ali A. Daddel
University of California - Davis
daddel@math.ucdavis.edu
June 15, 2021
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