Math 33AH: Linear Algebra and Applications (Honors)
Winter 2011
Time and Place: MWF 10:0010:50 am in MS 6201

Instructor: Ciprian Manolescu

Email: cm@math.ucla.edu

Office: MS 6921

Office Hours: Mondays 23pm, Fridays 11am12pm, and by
appointment

 Section: Tuesdays 1010:50 am in MS 6201
 Teaching
Assistant: Tye Lidman

Email: tlid@math.ucla.edu

Office Hours: Mondays 11am12pm 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,
twobytwo and threebythree 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, ranknullity
theorem, determinants, orthogonality, orthonormal bases, orthogonal
matrices, GramSchmidt process, QR factorization, leastsquares
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, 5.15.4, 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 inclass 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 makeup 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 1.13.3.
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,
5.15.4, and 6.16.3.
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, 111pm (Lidman) and 3:304:30pm (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 79 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, 10am12pm in MS 3931 (Lidman) and Wednesday Mar 16, 13pm 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 

