Linear Algebra and Applications

UNIVERSITY OF CALIFORNIA, LOS ANGELES - SUMMER 2022

MATH 33A:1 - Linear Algebra and Applications

Instructor : Pablo S. Ocal

Office hours : T 9:00-11:00 am

Teaching Assistant : Rushil Raghavan

Office hours : TR 8:00-9:00 am

Teaching Assistant : Alex Frederick

Office hours : TBD

Teaching Assistant : Benjamin Adams Thompson

Office hours : TBD

	Table of Contents
	1. Description
	2. Class Notes
	3. Schedule
	4. Homework
	5. Discussion
	6. Exams
	7. Resources

Description

The course on Linear Algebra and Applications will treat, among others, systems of linear equations, linear independence, bases and dimension, orthogonality, determinants, eigenvalues and eigenvectors, and matrix diagonalization. The prerequisites required for this course are covered in Math 3B, Math 31B, and Math 32A.

The course will have weekly classes on

Mondays, Tuesdays, and Wednesdays in Zoom Meeting 964 3894 8318, from 11:00 am to 12:50 pm.

The book we will be following is Linear Algebra with Applications (5th edition) by Otto Bretscher. We will be covering material in Chapters 1, 2, 3, 5, 6, 7, and 8. You may find all the information you will need on the Syllabus.

Class Notes

The following notes are a formal outline of the material we will be covering. These notes are not comprehensive nor are intended to be a substitute for the textbook or the lectures. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

MATH 33A Class Notes.

The following are additional materials closely related to the class notes.

Tentative Schedule

Jun 20	Sections 1.1, 1.2, 1.3, Introduction to Linear Systems, Matrices, Vectors, and Gauss-Jordan Elimination. On the Solutions of Linear Systems; Matrix Algebra. Notes.
Jun 21	Sections 1.3, 2.1, On the Solutions of Linear Systems; Matrix Algebra. Introduction to Linear Transformations and Their Inverses. Notes.
Jun 22	Sections 2.2, 2.3, Linear Transformations in Geometry. Matrix Products. Notes.
Jun 27	Sections 2.3, 2.4, Matrix Products. The Inverse of a Linear Transformation. Notes.
Jun 28	Sections 3.1, 3.2, Image and Kernel of a Linear Transformation. Subspaces of ℝⁿ; Bases and Linear Independence. Notes. Office hours.
Jun 29	Section 3.2, Subspaces of ℝⁿ; Bases and Linear Independence. Review. Notes.
Jun 30	Sections 1.1-1.3, 2.1-2.4, 3.1-3.2, Midterm 1.
Jul 4	Sections 3.3, 3.4, The Dimension of a Subspace of ℝⁿ. Coordinates. Notes.
Jul 5	Section 5.1, Orthogonal Projections and Orthonormal Bases. Notes. Office hours.
Jul 6	Sections 5.2, 5.3, Gram-Schmidt Process and QR Factorization. Orthogonal Transformations and Orthogonal Matrices. Notes.
Jul 11	Sections 5.3, 5.4, Orthogonal Transformations and Orthogonal Matrices. Least squares. Notes.
Jul 12	Sections 6.1, 6.2, Introduction to Determinants. Properties of the Determinant. Notes. Office hours.
Jul 13	Section 6.2, Properties of the Determinant. Review. Notes.
Jul 14	Sections 3.3-3.4, 5.1-5.4, 6.1-6.2, Midterm 2.
Jul 18	Sections 6.3, 7.1, Geometrical Interpretations of the Determinant; Cramer's Rule. Diagonalization. Notes.
Jul 19	Sections 7.1, 7.2, Diagonalization. Finding the Eigenvalues of a Matrix. Notes. Office hours.
Jul 20	Sections 7.3, 7.5, Finding the Eigenvectors of a Matrix. Complex Eigenvalues. Notes.
Jul 25	Sections 7.5, 8.1, Complex Eigenvalues. Symmetric Matrices. Notes.
Jul 26	Sections 8.2, 8.3, Quadratic Forms. Singular Values. Notes.
Jul 27	Section 8.3, Singular Values. Review. Notes.
Jul 28	Sections 1.1-1.3, 2.1-2.4, 3.1-3.4, 5.1-5.4, 6.1-6.3, 7.1-7.3, 7.5, 8.1-8.3, Final Exam.

Homework

There will be typically weekly homework. The assignments will be posted before Mondays at 9:00 am. The assignments will be due on Gradescope the following week, on Wednesday at 11:59 pm. The assignments and deadlines will be posted here. You are encouraged to work in groups.

Jun 20	Homework 0. Deadline: Jun 29.
Jun 27	Homework 1. Deadline: Jul 6.
Jul 4	Homework 2. Deadline: Jul 13.
Jul 11	Homework 3. Deadline: Jul 20.
Jul 18	Homework 4. Deadline: Jul 27.
Jul 18	Homework 5. Deadline: Jul 27.

Discussion

There will be typically weekly discussion sessions. These are thematic worksheets around a subject, intending to provide a deep dive into a challenging topic. The worksheets will be posted before Mondays at 9:00 am. The first starred problem will be due on Gradescope on Tuesday at 11:59 pm. The second starred problem will be due on Gradescope on Thursday at 11:59 pm. The worksheets and deadlines will be posted here. You are encouraged to work in groups.

Jun 28	Worksheet 1, Solutions.
Jul 5	Worksheet 2, Solutions.
Jul 12	Worksheet 3, Solutions.
Jul 19	Worksheet 4, Solutions.
Jul 26	Worksheet 5, Solutions

Exams

Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams here.

Jun 30-Jul 1	Midterm 1, Solutions, From 8:00 am to 8:00 am.
Jul 14-Jul 15	Midterm 2, Solutions, From 8:00 am to 8:00 am.
Jul 28-Jul 29	Final Exam, Solutions, From 8:00 am to 8:00 am.

The following are practice exams that you may use to prepare:

Resources

There are many resources available for a student at UCLA, I encourage you to use them and make the most out of them. Here are some materials specific to this course:

The Canvas forum can be found here. I encourage you to use this to post questions (anonymously if you wish), answers, and discuss the material presented in the lectures.
The open office hours at the Student Math Center can be found here.
The Math Success Program from the Community Programs Office can be found here.
The online calculator Wolfram|Alpha can be found here.

I also encourage you to form study groups with your classmates. However, please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions or copying others' work is absolutely useless.