Linear Algebra  Distance LearningPlease keep an eye on your
email for updates and messages from me.
Use the links below as needed to access materials and videos for your
class. Much of the content from the end of Chapter 4 through Chapter 8 was
organized and prepared during school closure in Spring 2020. Also, some older links
may not be available because of the Fall 2019 server shutdown.
Course Description (from SDSU General
Catalog): Math 254. Introduction to Linear Algebra. 3 units.
Prerequisite: Mathematics 151*. Matrix algebra, Gaussian elimination, determinants, vector spaces, linear
transformations, orthogonality, eigenvalues, and eigenvectors.
*At TPHS, students take Math 252/Calculus D before or
concurrently with Math 254/Linear Algebra.
General Information
Chapters 1, 2, 3
Systems of Linear Equations and Matrices, Determinants,
Vectors in 2Space and 3Space
 Notebook Assignments
 Quizzes
 Additional Notes and Support Materials
Chapter 4  Euclidean Vector Spaces
 Notebook Assignments: Chapters 4 & 5
 Quiz:
Quiz #3
Sections 4.1  4.3
 Additional Notes and Support Materials
 Matrix Transformations Mathematica Notebooks
(Coming Soon)
 End of Chapter 4: Spring 2020 Materials
for Asynchronous Distance Learning
Chapter 5  General Vector Spaces
Most of the below videos, links, and materials were prepared in Spring 2020
for asynchronous distance learning.
 Notebook Assignments: Chapters 4 & 5
 Lesson 1: Vector Spaces
 Lesson 2: Spanning, Linear Independence, Basis, and Dimension
 Lesson 3: Row Space, Column Space, and Nullspace
 Quiz #4
Sections 5.1  5.6
 Professor Dave Explains Videos for Review
I found these too late for this chapter, but if you are looking for
something to use for review, these could be useful.
Chapter 6  Inner Product Spaces
Most of the below videos, links, and materials were prepared in Spring 2020
for asynchronous distance learning.
 Notebook Assignments: Chapters 6, 7 & 8
(Note: Updated 02/02/2020)
 Lesson 1: 6.1 & 6.2 Inner Product Spaces
 Lesson 2: 6.3 Orthonormal Bases, GramSchmidt, and
QRDecomposition
 Lesson 3: 6.5 Orthogonal Matrices and Change of Basis

Quiz #5
Sections 6.1  6.5

Time for a Laugh: "Ma & Pa Kettle"
Chapter 7  Eigenvalues & Eigenvectors
Most of the below videos, links, and materials were prepared in Spring 2020
for asynchronous distance learning.
Chapter 8  Linear Transformations
Most of the below videos, links, and materials were prepared in Spring 2020
for asynchronous distance learning.
 Notebook Assignments: Chapters 6, 7 & 8
(Note: Updated 02/02/2020)
 Lesson: 8.1 & 8.2 General Linear Transformations
Additional Support
In Spring 2020 I put together this list of video links as
additional resources for my students. At the time we focused primarily on
Chapters 4 through 8, however these channels should have good support for
earlier concepts too.
 Essence of Linear Algebra Video Series:
Essence of Linear Algebra on YouTube
I've heard good things about this series for helping to visualize and
understand the big ideas. I have not watched all of these and note that the
series addresses topics in a different order than we do.
 Professor Dave Explains Video Series:
Linear Algebra on YouTube by
Professor Dave Explains
I have not watched all of these. What I have seen looks like they would
be good support for lessons and review. I wish I had found these earlier
instead of while preparing Chapter 7.
 Sheldon Axler Video Series (to Support "Chapter 5 General Vector Spaces")
Of all of the video series I found, this one seems to be most similar to
what we do in the first four sections of Chapter 5 and uses essentially the
same definitions for Vector Space, Subspace, Span, Linear Independence,
Basis, and Dimension. Note: I have not fully watched all of these videos,
but skimmed them to check their definitions.
The notation is a little different and you do not need to worry about
complex numbers. I think these will be good support if you are looking for
additional explanations of the key definitions in this part of the chapter.
 This one has some potential...Just posting it for now, but I really
haven't looked at it yet.
http://www.math.brown.edu/~sswatson/classes/math0520/index.html
 This is UCSB's list that looks like they gleaned videos from across the
internet on different topics. Again, I haven't fully explored it yet.
http://web.math.ucsb.edu/oml/4A.html
 Top 
Additional Notes
(Original links...Keeping here for my reference)
The above course notes, assignments, and quizzes are for the Linear
Algebra (SDSU Math 254)
classes I teach at
Torrey Pines High School. I wrote and modified
these files over several semesters. Much
of the work is my own; however, I borrowed several examples
and diagrams from the textbooks* my classes used while
I taught the course. These notes,
assignments, and quizzes are free for use by my current
and former students. If other Linear Algebra students and teachers
find these notes useful, I would be happy to know that
my work was helpful.  Abby Brown
*Elementary Linear Algebra, 8th edition,
Howard Anton, ©2000 John Wiley & Sons, Inc., ISBN 0471170550. (Chapter, section, page, and formula numbers refer to this text.)
*Elementary Linear Algebra: Student Solutions Manual, 8th edition,
Elizabeth M. Grobe and Charles A. Grobe, Jr., ©2000 John Wiley & Sons,
Inc., ISBN 0471382493.
*And a few additional Linear Algebra textbooks
that I own or borrowed from friends.
Most of the links are PDF files that can be read with Adobe Reader. If you have
trouble downloading the files, try rightclicking and selecting "Save
Target As..." If you have trouble printing, try printing five or so pages
at a time rather than all at once. For best results, use the most current
version of Adobe Reader.