# MAT22A Linear Algebra - Winter 2011

## News and announcements

• (3/19/11) Have an enjoyable spring break, and successful spring quarter!
• (3/19/11) Here is a chart showing the distribution of final grades in the course:
• (3/19/11) Final grades have been uploaded to the system and should be visible soon on SmartSite/SIS. A total score (in the range 0-100) was computed as a weighted average of the midterms, final, webwork homework and written homework assignments, as described in the course grading policy (this total score can be seen on the course SmartSite grades, under "Final Score"). The letter grades were computed from the total score according to the following cutoff ranges:  A+ 97-100 A 92-96.999 A- 89-91.999 B+ 86-88.999 B 83-85.999 B- 81-82.999 C+ 79-80.999 C 77-78.999 C- 74-76.999 D+ 71-73.999 D 68-70.999 D- 65-67.999 F 0-64.999
• (3/11/11) Click here for a set of practice questions for the final exam. The final exam will have roughly the same length and difficulty level. Click here for the solutions.
• (3/3/11) The fifth and final written homework assignment will be due on Friday 3/11 (note the unusual day) before class starts. The assigned problems are:
• Lecture 21: problems 2, 3.
• Lecture 22: problem 3.
• Lecture 23: problem 4.
• Lecture 24: problem 1.
• (2/23/11) The grades for the second midterm can now be accessed through SmartSite. The average grade was 86 and the standard deviation was 11. Here is a chart showing the grade distribution:

• (2/17/11) The fourth written homework assignment will be due on Wednesday 3/2 (note the unusual day) before class starts. The assigned problems are:
• Lecture 17: problems 2, 3.
• Lecture 18: problem 2.
• Lecture 19: problems 3, 4.
• Lecture 20: problems 1, 4, 5.
• (2/11/11) Click here for the solutions to the second practice question set.
• (2/10/11) Click here for a set of practice questions for next Wednesday's midterm exam. Solutions will be posted soon. The exam will cover lectures 8 through 16 (except lecture 11) in the lecture notes and any related material covered in class. Like the first midterm, the exam will be 45 minutes long and will be a closed book exam. Don't forget to bring an exam blue book and your student ID.
• (2/5/11) The third written homework assignment will be due on Monday, 2/14 before class starts. The assigned problems are:
• Lecture 10: problem 3.
• Lecture 12: problem 2.
• Lecture 13: problem 1.
• Lecture 14: problem 1.
• Lecture 15: problems 1, 3.
• Lecture 16: problems 1, 2.
• (2/2/11) The grades for the midterm exam can now be accessed through SmartSite. The average grade was 75 and the standard deviation was 14. Here is a chart showing the grade distribution:

• (1/20/11) The second written homework assignment will be due on Monday, 1/31 before class starts. The assigned problems are:
• Lecture 6: problems 2, 3, 4.
• Lecture 7: problems 1, 2.
• Lecture 8: problems 2, 3, 5.
• Lecture 9: problems 1, 3, 4.
• (1/20/11) Click here for a set of practice questions for next week's midterm exam. Solutions will be posted in the next few days. The exam will be 45 minutes long and will be a closed book exam.
• (1/07/11) The first written homework assignment will be due on Wednesday, 1/19 (since Monday 1/17 is a holiday). The assigned problems are taken from the "Review Problems" at the end of each lecture in the lecture notes. The problems to be handed in (in class before the lecture starts) are:
• Lecture 1: problems 1, 3.
• Lecture 2: problems 1, 2, 3.
• Lecture 3: problems 1, 3.
• Lecture 4: problems 1, 2, 3.
• Lecture 5: problems 1, 2.
• A few problems will be graded. The problems will be graded both for correctness and quality of presentation.
• (1/03/11) The WeBWork problem sets for the first week are now open. For instructions on logging in refer to the Getting Started Guide. If you are having difficulties using WeBWork, consult the Help Wiki and if you cannot find an answer to your question, email Rohit Thomas, the math department's dedicated WeBWork T.A.
• (12/29/10) Important information on MAT22AL: Please read this important note on MAT22AL, the linear algebra computer lab class that is a prerequisite for this class for all students except those who have taken Eng 6.

## General Information

 Instructor details: Dan Romik Mathematical Sciences Building 2218 tel: 530-554-1498 email: For more information go to my home page Lectures: MWF 5:10-6:00 at Young 198 Office hours: F 11:00-11:50, F 1:10-2:00 (at my office, MSB 2218), or by appointment TAs: Dustin Mayeda (MSB 2145 -- office hours: T 2:30-4:30) Chuan Qin (MSB 3204 -- office hours: R 9:30-11:30) Jing Xia (MSB 2127 -- office hours: F 9:00-11:00)

## Textbook and Syllabus

The class will follow the free lecture notes Linear Algebra in Twenty Five Lectures, by Tom Denton and Andrew Waldron. Additional reading material that is complementary to (and referred to by) the lecture notes are the two free online textbooks Linear Algebra by Jim Hefferon and A First Course in Linear Algebra by Rob Beezer.

### Detailed list of topics

Linear Systems, Vectors and Linear Transformations
Solving Linear Systems
Solution Sets
Vectors in Space, n-Vectors
Vector Properties
Vector Spaces
Linear Transformations
Matrices
Matrix Properties
Inverse Matrices
LU Decomposition
Elementary Matrices and Determinants
Properties of Determinants
Eigenvalues and Eigenvectors
Subspaces, Spanning Sets
Linear Independence
Bases and Dimension
Diagonalization
Orthonormal Bases
Diagonalizing Symmetric Matrices
Kernel Rank and Range
Orthogonal Complements and Gram Schmidt
Least Squares

## Homework

There are two kinds of homework:
1. Online homework that you will prepare using the WeBWork system. The WeBWork problem sets are themselves divided into:
• Very short reading comprehension sets. The problems for each lecture are due by the beginning of the next lecture.
• A weekly "skills" set of more thorough problems covering the previous week's material. The skills set is due by the time of next Friday's lecture.
2. Written homework that you will hand in in class on Monday every two weeks. The problems appear in the lecture notes at the end of each lecture chapter.

## Exams

There will be two in-class midterm exams and a final exam.

Exam dates
 First exam: Wednesday, Jan. 26 Second exam: Wednesday, Feb. 16 Final exam: Wednesday, Mar. 16, 3:30-5:30 PM