# SYLLABUS

## Linear Algebra (Math 544, Section 3) Spring 2001, USC

Lecture
Tu Th 4:30-5:45 pm LC 115
Instructor
Check the course web site periodically for revised versions of this syllabus, and to obtain homework assignments and copies of old tests and quizzes.

Course Description
This is an introduction to linear algebra and its applications. Main topics include matrix algebra, solution of linear systems, determinants, notions of vector space, basis, dimension, linear transformations, eigenvalues, and diagonaliztions. We will develop at each step the applications of these concepts to a range of problems in Mathematics, Engineering, and Economics.

Prerequisites
Math 241--familiarity with vectors.

Textbook
Linear Algebra and it Applications, by David C. Lay, Second Edition.

Homework and Quizzes
There will be weekly homework assignments due every Tuesday. Late homeworks will not be accepted.

Also, there will be weekly quizzes every Thursday. No calculators, textbooks, or notes will be allowed during quizzes. You should save copies of these quizzes as they are a very good source for preparing for the final and midterms. There may be a number of practice quizzes during the lectures as well.

Doing the homework problems is the most important part of any math class. You may work with a group of your classmates if you are all at about the same level; however, you should definitely try to do many problems on your own. Further, try to practice doing at least some of the problems in settings which resemble that of the test and quizzes, i.e., without using your calculator or constantly referring to the textbook.

You should make a sincere effort to keep up with your reading assignments.
 Dates Lectures Jan 1618 TTH 1.11.2 Systems of Linear Equations Row Reduction and Echelon Forms 2325 TTH 1.31.4 Vector EquationsThe Matrix Equation Ax=b 30 T 1.5 Solutions of Linear Systems Feb 1 TH 1.6 Linear Independence 68 TTH 1.71.8 Intro to linear transformationsMatrix of a linear transformation 1315 TTH 1.9. Linear Models in ScienceMidterm 1 2022 TTH 2.12.2 Matrix OperationsThe Inverse of a Matrix 27 T 2.3 Characterizations of Invertible Matrices Mar 1 Th 2.8 Applications to Computer Graphics 68 TTH 2.92.9 Subspaces of R^nSubspaces of R^n 1315 TTH . . Spring BreakSpring Break 2022 TTH 3.13.2, 3.3 Intro to Determinants Properties, Volume 2729 TTH .. ReviewMidterm 2 Apr 35 TTH 4.14.2, 4.3 Vector Spaces and SubspacesNull Spaces, Column Spaces, and Bases 1012 TTH 4.4 4.5 Coordinate SystemsThe Dimension of a vector Space 1719 TTH 4.75.1, 5.2 Change of basisEigenvalues, Characteristic Equation 2426 TTH 5.3. DiagonalizationFibonacci Sequence May 1 T . Review 9 W . Final Exam

Assignments
You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
 Homework # Due Date Problems 1 Jan 23 1.1) 2, 6, 8, 12, 14, 24, 28, 34, 35; 1.2) 2, 6, 10, 14, 31, 32, 33, 35. 2 Jan 30 1.3) 6, 8, 10, 12, 14, 23, 29; 1.4) 4, 8, 10, 12, 14, 18. 3 Feb 6 1.5) 2, 6, 14, 16, 26, 36, 38; 1.6) 4, 6, 10, 20, 22, 26, 28, 30, 32, 34, 36. 4 Feb 13 1.7)2, 4, 10, 12, 14, 16, 18, 20, 24, 30, 34; 1.8) 2, 6, 10, 12, 18, 24, 26, 28, 33. 5 Feb 20 1.9)2, 4, 10, 12; Chap 1 Supplementary Exercises) 1, 3, 6, 11. 6 Feb 27 2.1)2, 4, 8, 12, 16, 20, 24, 26, 30; 2.2) 4, 6, 10, 12, 13, 25, 26. 7 Mar 6 2.2)23, 24, 30, 32, 34; 2.3)4, 6, 8, 14, 16, 26, 28, 34; 2.8)2, 4, 6, 8, 10, 11. 8 Mar 20 2.8)7,14; 2.9)2, 4, 6, 8, 10, 16, 18, 22, 24, 26, 28, 34. 9 Mar 27 3.1)4, 10, 16, 20, 22, 28, 34, 42; 3.2)16, 18, 22, 26, 28, 31, 32, 33, 34, 35; 3.3) 20, 24, 29, 30, 31. 10 Apr 3 Chap 3 Supplementary Exercises) 4, 6, 7, 9, 12. 11 Apr 10 4.1) 2, 4, 6, 8, 10, 12, 14, 24, 26, 28, 30; 4.2) 2, 6, 8, 10, 26, 28, 34; 4.3) 2, 4, 6, 11, 12, 23, 24. 12 Apr 17 4.4) 4, 6, 12, 14, 28; 4.5) 2, 4, 9, 22, 24, 27, 28. 13 Apr 24 4.7) 8, 10, 14; 5.1) 2, 6, 10, 24, 32; 5.2) 4, 8, 10, 16, 25. 14 May 1 5.3) 2, 8, 10, 24; Handout) 2, 3, 4, 5, 7, 8.

Tests and Exams
There will be two midterms, on Thursday Feb 15 and on Thursday Mar 29. The final exam will be on Wednesday May 9 at 5:30 pm. No calculators, or notes will be allowed during the exams. Note: bring a bluebook to the exams.