33A (Lec. 1), Linear Algebra and Applications

Textbook: Linear Algebra (fifth edition) by O. Bretscher.

Instructor: Monica Visan, 6167 Math Sciences Building.

Office Hours: Tuesday 10am-12pm or by appointment.

Exams:

• Midterm 1: Wednesday, February 8th, in class.
• Midterm 2: Wednesday, March 1st, in class.
• Final: Thursday, March 23rd, 8:00-11:00am.

Midterm 1: will cover the material presented in the first 11 lectures; see the table below. You can find a practice midterm here.

Midterm 2: will cover all the material presented in the first 19 lectures; see the table below. You can find a practice midterm here.

Final: will cover all the material presented this quarter. You can find a practice final here.

Homework: There will be weekly homework. It is due in class on Fridays. It will be posted on this webpage the weekend before it is due. Further information is given below.

• No late homework will be accepted.
• The reader will grade three problems, each out of five points.
• Up to five further points will be awarded based on the proportion of the remaining problems that are completed.
• Write your name, ID number, and TA section at the top of the first page.
• Staple your pages!
• Homework will be returned in TA section.
• The weakest homework score will be omitted.
• While you may collaborate on the homework, the final version needs to be written in your own words. The loaning or copying of solutions is strictly forbidden.

Grading: Homework: 10%; Midterm 1: 20%; Midterm 2: 20%; Final: 50%. No exceptions.

Teaching Assistants:

• Madeleine Bulkow
• Alex Mennen
• Laurent Vera

Student Math Center

Syllabus: The following table will be updated as we progress through the course.

Lecture	Book Sections	Topics
1	1.1-2	Linear systems, Gauss-Jordan elimination
2	1.3	Gauss-Jordan elimination, matrix algebra
3	2.1-2	Linear transformations
4	2.2	Linear transformations in Geometry
5	2.3	Matrix algebra, products
6	2.3-4	Matrix algebra, inverses
7	2.4, 3.1-2	Matrix inverses, kernel and image of linear transformations, subspaces of Rn
8	3.1-2	Linear independence, bases
9	3.1-3	Linear independence, bases for the kernel and image of a linear transformation, dimension.
10-11	3.4	Coordinates
12	5.1-2	Orthogonality, orthonormal bases, Gram-Schmidt process
13	5.2	Gram-Schmidt process, QR-factorization
14	5.1 and 5.4	Orthogonal projection, least squares methods
15	5.1-4	Orthogonal transformations, orthogonal matrices
16-19	6.1-3	Determinants
20	7.1-2	Eigenvalues and eigenvectors, computing eigenvalues
21-22	7.3	Computing eigenvectors, diagonalization of matrices
23-26	8.1-3	Symmetric matrices, quadratic forms, SVD (singular-value decomposition)

Homework Problems:

• Homework 1 is due Friday, Jan. 13th, in class.
• Homework 2 is due Friday, Jan. 20th, in class.
• Homework 3 is due Friday, Jan. 27th, in class.
• Homework 4 is due Friday, Feb. 3rd, in class.
• Homework 5 is due Friday, Feb. 10th, in class.
• Homework 6 is due Friday, Feb. 17th, in class.
• Homework 7 is due Friday, Feb. 24th, in class.
• Homework 8 is due Friday, Mar. 3rd, in class.
• Homework 9 is due Friday, Mar. 10th, in class.
• Homework 10. Do not submit it for grading.