MAT 331 Elementary Linear Algebra, # 41039, Fall 2002

Class meets MWF 11:30-12:20 in EAC 501.

Instructor: Prof. Serban Raianu, office: NSM A-135, office phone number: (310) 243-3139,

e-mail address:, office hours: Tuesday 18:00-19:00 in the Math Lab SAC 1115; in my office: MWF: 12:30-13:30,  or by appointment.

Course Description: MAT 331, Elementary Linear Algebra,  covers Chapters 1-7 from the textbook: linear equations, vector spaces, matrices, linear transformations, determinants, eigenvalues, eigenvectors, etc.

Text: Elementary Linear Algebra, 4th edition by Larson and Edwards, Houghton Mifflin, 2000.

Objectives: After completing MAT 331 the student should be able to: solve systems of linear equations; add, multiply matrices, find the inverse of an invertible matrix; evaluate determinants; work with vectors, identify bases of vector spaces, find eigenvalues and eigenvectors of linear transformations.

Prerequisites: MAT 271 or equivalent with a grade of "C" or better.

Grades: Grades will be based on three in‑class full‑period examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, and other assignments (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will be collected every class meeting, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every class meeting, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q. There are also 5 points awarded for attendance and class participation, this portion of the grade is denoted by A. The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F. 

To determine your final grade  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

        A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

        C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.

Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with your instructor, who may then substitute the relevant score from your final examination for the missing grade.

Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see their instructor as soon as possible.

Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Technology: Symbolic calculators, such as TI-89 or TI-92 are acceptable for this course.


Tentative schedule: 

M 8/26: 1.1. Introduction to Systems of Linear Equations: (odd numbers only) 1-3,7-9,13-15,27-33,37-45

W 8/28: 1.2. Gaussian & Gauss-Jordan Elimination: (odd only) 1-31,37-39

F 8/30: 2.1. Operations with Matrices: (odd) 1-27

M 9/2: Labor Day

W 9/4: 2.2. Properties of Matrix Operations: (odd) 1-19

F 9/6: 2.2. Properties of Matrix Operations: (odd) 23-31,35,37

M 9/9: 2.3. The Inverse of a Matrix: (odd) 1-19,25 a),c), 27) a), 29-31

W 9/11: 2.4. Elementary Matrices: (odd) 1-17,21-27

F 9/13: 2.4. Elementary Matrices: (even) 2-16,22-26

M 9/16 : 3.1. The Determinant of a Matrix: (odd) 1-15,19-31,37-41

W 9/18: 3.2. Evaluation of a Determinant Using Elementary Operations: (odd) 1-27

F 9/20: 3.3. Properties of Determinants: (odd) 1-13

M 9/23: Review

W 9/25: Exam I

F 9/27: analyzing exam I.

M 9/30: 4.1. Vectors in Rn : (odd) 9-27

W 10/2: 4.2. Vector Spaces: (odd) 1-23

F 10/4: 4.3. Subspaces of Vector Spaces: (odd) 1-3,15-19

M 10/7: 4.4. Spanning Sets and Linear Independence: (odd) 1-27

W 10/9: 4.5. Basis and Dimension: (odd) 9-15,21-33

F 10/11: 4.5. Basis and Dimension: (odd) 35-51

M 10/14: 4.6. Rank of a Matrix and Systems of Linear Equations: (odd) 1-21,31-33

W 10/16: 4.7. Coordinates and Change of Basis: (odd) 1-19

F 10/18: 5.1. Length and Dot Product in Rn : 1-19,23-29,55-59

M 10/21: 5.2. Inner Product Spaces: (odd) 1-7,13,31-33,41-43

W 10/23: Review

F 10/25: Exam II

M 10/28: analyzing exam II.

W 10/30: 5.3. Orthonormal Bases: Gram-Schmidt Process: (odd) 1-9,19-25

F 11/1: 5.5. Applications of Inner Product Spaces: (odd) 1-5,11-13,15-17

M 11/4: 6.1. Introduction to Linear Transformations: (odd) 1-3,7-11,15-19,21-25

W 11/6: 6.2. The Kernel and Range of a Linear Transformation: (odd) 1-11

F 11/8: 6.2. The Kernel and Range of a Linear Transformation: (odd) 13-19,25-31

M 11/11: 6.3. Matrices for Linear Transformations: (odd) 1-11

W 11/13: 6.3. Matrices for Linear Transformations: (odd) 13-23,31-33

F 11/15: 7.1. Eigenvalues and Eigenvectors: (odd) :1-11

M 11/18: 7.1. Eigenvalues and Eigenvectors: (odd) 13-23

W 11/20: 7.2. Diagonalization: (odd) 1-9

F 11/22: 7.2. Diagonalization: (odd) 11-21

M 11/25: 7.3. Symmetric Matrices and Orthog. Diagonalization: (odd) 1-15,21-25

W 11/27: Review

F 11/29: Thanksgiving break.

M 12/2: Exam III

W 12/4: analyzing exam III

F 12/6: Review

Final exam: Wednesday, December 11, 11:30-13:30.