Table of Contents | |

1. Description | |

2. Class Notes | |

3. Schedule | |

4. Homework | |

5. Discussion | |

6. Exams | |

7. Resources |

UNIVERSITY OF CALIFORNIA, LOS ANGELES - FALL 2023

MATH 33A:1 - Linear Algebra and Applications

Instructor : Pablo S. Ocal

Office hours : W 9:00-10:30 am (MS 6627)

Teaching Assistant : Adam Zheleznyak

Office hours : T 10:30-11:30 am (MS 2905)

Teaching Assistant : Benjamin Goldman

Office hours : T 9:00-10:00 am (MS 2963), R 9:00-10:00 am (MS 3974)

Teaching Assistant : Victoria Quijano

Office hours : T 3:15-4:15 pm (MS 3903)

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, Wednesdays, and Fridays in MS, room 4000A, from 8:00 to 8:50 am.**

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.

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

Tentative Schedule

Sep 29 | Sections 1.1, 1.2, Introduction to Linear Systems, Matrices, Vectors, and Gauss-Jordan Elimination. Notes. |

Oct 2 | Section 1.3, On the Solutions of Linear Systems; Matrix Algebra. Notes. |

Oct 4 | Section 2.1, Introduction to Linear Transformations and Their Inverses. Notes. |

Oct 6 | Section 2.2, Linear Transformations in Geometry. Notes. |

Oct 9 | Section 2.3, Matrix Products. Notes. |

Oct 11 | Section 2.4, The Inverse of a Linear Transformation. Notes. |

Oct 13 | Section 3.1, Image and Kernel of a Linear Transformation. Notes. |

Oct 16 | Section 3.2, Subspaces of ℝ ^{n}; Bases and Linear Independence. Notes. |

Oct 18 | Section 3.3, The Dimension of a Subspace of ℝ ^{n}. Notes. |

Oct 20 | Section 3.4, Coordinates. Notes. |

Oct 23 | Sections 1.1-1.3, 2.1-2.4, 3.1-3.4, Review. |

Oct 25 | Sections 1.1-1.3, 2.1-2.4, 3.1-3.4, Midterm 1. |

Oct 27 | Section 5.1, Orthogonal Projections and Orthonormal Bases. Notes. |

Oct 30 | Section 5.1, Orthogonal Projections and Orthonormal Bases (continued). Notes. |

Nov 1 | Section 5.2, Gram-Schmidt Process and QR Factorization. Notes. |

Nov 3 | Section 5.3, Orthogonal Transformations and Orthogonal Matrices. Notes. |

Nov 6 | Section 5.4, Least squares. Notes. |

Nov 8 | Section 6.1, Introduction to Determinants. Notes. |

Nov 13 | Section 6.2, Properties of the Determinant. Notes. |

Nov 15 | Section 6.3, Geometrical Interpretations of the Determinant; Cramer's Rule. Notes. |

Nov 17 | Sections 5.1-5.4, 6.1-6.3, Review. |

Nov 20 | Sections 5.1-5.4, 6.1-6.3, Midterm 2. |

Nov 22 | Section 7.1, Diagonalization. Notes. |

Nov 27 | Section 7.2, Finding the Eigenvalues of a Matrix. Notes. |

Nov 29 | Section 7.3, Finding the Eigenvectors of a Matrix. Notes. |

Dec 1 | Section 7.5, Complex Eigenvalues. Notes. |

Dec 4 | Section 8.1, Symmetric Matrices. Notes. |

Dec 6 | Section 8.2, Quadratic Forms. Notes. |

Dec 8 | Section 8.3, Singular Values. |

Dec 14 | 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 Friday at 11:59 pm. The assignments and deadlines will be posted here. You are encouraged to work in groups.

Oct 2 | Homework 0. Deadline: Oct 11. |

Oct 2 | Homework 1. Deadline: Oct 13. |

Oct 9 | Homework 2. Deadline: Oct 20. |

Oct 16 | Homework 3. Deadline: Oct 27. |

Oct 23 | Homework 4. Deadline: Nov 3. |

Oct 30 | Homework 5. Deadline: Nov 10. |

Nov 6 | Homework 6. Deadline: Nov 17. |

Nov 13 | Homework 7. Deadline: Dec 1. |

Nov 20 | Homework 8. Deadline: Dec 1. |

Nov 27 | Homework 9. Deadline: Dec 8. |

Dec 4 | Homework 10. Deadline: Dec 8. |

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 while having readily available feedback. The starred problem(s) 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.

Oct 2 | Worksheet 1, Solutions. Deadline: Oct 5. |

Oct 9 | Worksheet 2, Solutions. Deadline: Oct 12. |

Oct 16 | Worksheet 3, Solutions. Deadline: Oct 19. |

Oct 23 | Worksheet 4, Solutions. Deadline: Oct 26. |

Oct 30 | Worksheet 5, Solutions. Deadline: Nov 2. |

Nov 6 | Worksheet 6, Solutions. Deadline: Nov 9. |

Nov 13 | Worksheet 7, Solutions. Deadline: Nov 16. |

Nov 20 | Worksheet 8, Solutions. Deadline: Nov 30. |

Nov 27 | Worksheet 9, Solutions. Deadline: Nov 30. |

Dec 4 | Worksheet 10, Solutions. Deadline: Dec 7. |

Exams

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

Oct 25 | Midterm 1, Solutions, MS 4000A from 8:00 to 8:50 am. |

Nov 20 | Midterm 2, Solutions, MS 4000A from 8:00 to 8:50 am. |

Dec 14 | Final Exam, MS 4000A from 3:00 to 6:00 pm. |

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 peer learning facilitator from the
**Academic Advancement Program**is Emma Lu. - The peer learning facilitator from the
**UCLA Athletics Academic Excellence**is Devyn Chun. - The Math Success Program from the
**Community Programs Office**can be found**here**. - The Frequently Asked Questions of the Undergraduate Math Council can be found
**here**. - The online calculator Wolfram|Alpha can be found
**here**.

Here are some general materials about the Department of Mathematics, the College of Physical Sciences, and UCLA:

- The Campus Resources document maintained by
**Britney Robinson**can be found**here**. - The Frequently Asked Questions of the Undergraduate Math Council 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.