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

Lectures: MWF 12:00-12:50pm in HUMANTS A51.

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

Instructor: Monica Visan, 6167 Math Sciences Building.

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


Bring student ID to both midterms and the final.
No calculators, notes, or books will be permitted in any exam.
There will be no make-up exams.

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.

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

Teaching Assistants:

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: