# Math 33AH: Linear Algebra and Applications (Honors)

Winter 2011

Time and Place: MWF 10:00-10:50 am in MS 6201

 Instructor: Ciprian Manolescu E-mail: cm@math.ucla.edu Office: MS 6921 Office Hours: Mondays 2-3pm, Fridays 11am-12pm, and by appointment Section: Tuesdays 10-10:50 am in MS 6201 Teaching Assistant: Tye Lidman E-mail: tlid@math.ucla.edu Office Hours: Mondays 11am-12pm in MS 3931

Web page: http://www.math.ucla.edu/~cm/33ah.1.11w/index.html

Prerequisites: Math 3B, 31A, 32A, or 32AH, preferably with a grade of at least A-. Completion of Math 32AH and 97 (as part of the Merit Track in mathematics) is recommended, but not required.

Students in the course should have covered the following topics in previous high school and college mathematics courses: solving linear systems of equations, matrices, matrix multiplication, two-by-two and three-by-three determinants, complex numbers, complex polynomials, the fundamental theorem of algebra. This background material is reviewed in the course, though briefly.

Course description: This is an honors introductory course in linear algebra. Although we will cover the same material as in Math 33A, the problem sets and the exams will be more difficult.

Topics to be covered are: systems of linear equations, associated matrix equations, row reduction of a matrix, linear transformations,invertible matrices, subspaces, linear independence, bases, dimension, row space, column space, rank-nullity theorem, determinants, orthogonality, orthonormal bases, orthogonal matrices, Gram-Schmidt process, QR factorization, least-squares approximation, normal equations, eigenvalues, eigenvectors, similarity, diagonalization, applications to discrete dynamical systems, diagonalization of symmetric matrices, applications to quadratic forms, singular value decomposition.

Textbook: O. Bretscher, Linear Algebra with Applications, 4th Edition, Pearson Prentice Hall, 2009. The plan is to cover Chapters 1, 2, 3, 5.1-5.4, 6, 7, and 8 from the textbook. We will follow the official course syllabus closely.

Grading: 40% final, 25% best score of two midterms, 10% lowest score of two midterms, 25% homework.

Exams: There will be two in-class midterms: one on Friday, January 28, and the other on Wednesday, February 23. The final exam is scheduled for Thursday, March 17, 11:30 AM - 2:30 PM.

No make-up exams will be given, except in case of a documented emergency. No books, notes or calculators will be allowed on the exams.

The first midterm will cover the material in Sections 1.1-3.3. It will be similar in format to the following practice midterm 1.
Here are the solutions to the first midterm.

The second midterm will cover the material in Sections 3.4, 5.1-5.4, and 6.1-6.3. It will be similar in format to the following practice midterm 2. There will be no office hours on Monday Feb 21 (Presidents' Day). Instead, we will have office hours on Tuesday Feb 22, 11-1pm (Lidman) and 3:30-4:30pm (Manolescu).
Here are the solutions to the second midterm.

The final exam is cumulative, but with more focus on the later material. Roughly half of the problems on the final will be on the sections covered on the two midterms, and half on the material after the second midterm. The exam will be similar in format to the following practice final.

Tye Lidman will run a review session for the final exam on Tuesday March 15, from 7-9 PM, in MS 5137. The last homework is due at the beginning of the final exam. Special office hours during the final week: Tuesday Mar 15, 10am-12pm in MS 3931 (Lidman) and Wednesday Mar 16, 1-3pm in MS 6921 (Manolescu). There will be no office hours on Monday.

Here are the solutions to the final.

Homework: Homework will be assigned every week and will be due in section on Tuesday. The lowest homework score will be dropped.

The homework assignments will be posted on the web page. You are encouraged to talk about the problems with other students, but you should write up the solutions individually. You should acknowledge the assistance of any book, student or professor. No late homework will be accepted.

Problem Set Due Read Exercises Solutions
1 January 11 §1.1, 1.2, 1.3
 §1.1: 34, 42 §1.2: 6,8,44,46 §1.3: 4,14,26,28
Solution Set 1
2 January 18 §2.1, 2.2, 2.3, 2.4
 §2.2: 20, 22, 26 §2.3: 4, 20, 32 §2.4: 6, 30, 76, 82
Solution Set 2
3 January 25 §3.1, 3.2, 3.3
 §3.1: 34, 38, 44, 50 §3.2: 6, 32, 36 §3.3: 20, 30, 38
Solution Set 3
4 February 8 §3.4, 5.1, 5.2
 §3.4: 10, 58, 66, 72 §5.1: 28, 30 §5.2: 4, 18, 32, 34
Solution Set 4
5 February 15 §5.3, 5.4, 6.1
 §5.3: 32, 54, 60 §5.4: 16, 20, 32 §6.1: 20, 44, 56, 60
Solution Set 5
6 February 23 §6.2, 6.3
 §6.2: 6, 8, 31, 50 §6.3: 2, 10, 22, 30, 36, 38
Solution Set 6
7 March 8 §7.2, 7.3, 7.4, 7.5
 §7.2: 22, 40 §7.3: 14, 20, 52 §7.4: 30, 32 §7.5: 16, 28, 48
Solution Set 7
8 Thursday March 17 §8.1, 8.2, 8.3
 §8.1: 24, 38, 42 §8.2: 10, 20, 28 §8.3: 14, 20, 26, 30