MTH 215/01-URI
Fall 2009

Text:   Linear Algebra (Third Edition) by David Lay

Instructor: M. Kulenovic           Office:  Lippitt Hall 200A
Phone:  874-4436    Email:

Online information: or
Office Hours: MTW 11-12, and by arrangement.

Time: MWF 10-10:50

Students who require accommodations and who have documentation from Disability Services (874-2098) should make arrangements with me as soon as possible.

Topics: vectors, matrices, linear systems, linear transformations, vector spaces, determinants, eigenvalues, eigenvectors.   There are many applications of linear algebra to problems in many areas of math and science.  We will look at applications in order to motivate the study of linear algebra.

Calculators: The recommended calculator is TI-89 or TI-92. TI-83, TI-84 and TI-86 could be also used.

Illness Due to Flu

The H1N1 Flu Pandemic may impact classes this semester.  If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours.  So, if you exhibit such symptoms, please do not come to class.  Notify me at 874-4436 or of your status, and we will communicate through the medium we have established for the class.  We will work together to ensure that course instruction and work is completed for the semester.


The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness.  These include:  covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick.  For more information, please view  URI information on the H1N1 will be posted on the URI website at, with links to the site.


Grading: Your grade will be based on three tests, a final exam, and classwork as follows:

Three tests at 100 points each 300 points 
Final exam 150 points
Classwork 150 points
Maple Projects
100 points
Total 700 points

Tests and the final exam:  The tests will be given in the class A comprehensive final exam will be given during the final exam period. Time and place will be announced later. The exams will reflect the variety of the homework problems. The best way to prepare for the exams, and to develop confidence in your ability to solve problems, is to work on the homework problems as suggested. Some problems may be done in class or as homework, as your instructor chooses. No makeups for exams will be given unless you have a University sanctioned excuse. 

Classwork: The distribution of the 150 points will be decided by your instructor. It will include quizzes and class participation.


Homework:  Homework plays a central role in the class and in your understanding of the material. It is fair to say that most of the learning that you achieve during any math course is from your homework. 

Read the textbook: An important part of your mathematical education is acquiring the knack of learning mathematics on your own, from books.  You may not be used to reading mathematics texts, but you will be actively encouraged to read this one. By reading the text before class, even if you don’t understand everything the first time, you will have a better chance of making good use of your time in class.  Reading the text after class is a good way of reinforcing the material in the lecture, nailing down what questions you need to ask in the next class, and learning material that was not gone over during class time.  The text is well written, with the beginning linear algebra student in mind. Linear algebra is much easier if you keep up with the classe and homework.  You also retain the material longer and better if you review material frequently rather than just studying at exam time. 

Week Sections Suggested Homework Problems Exams/Events
Systems of Linear Equations
Row Reduction and Echelon Forms
1.2 1,3,7,11,19,25,29,31 
Vector Equations 1.3 1,5,9,11,13,17,25

The Matrix Equation Ax = b
1.4 1,7,9,15, 21,23,25,29,37
Solution Sets of Linear Systems 1.5 1,5,11,15,19,27,31,35
Linear Independence
Introduction to Linear Transformations 1.8 1,5,7,9,11,19,25,35
The Matrix of a Linear Transformation 1.9 1,5,7,9,15,19,37
Matrix Operations 2.1 1,5,9,17,23,31

The Inverse of a Matrix
2.2 1,3,7,8,11,13,17,19,29,31,35 
Characterizations of Invertible Matrices 2.3 1,5,7,11,17,27,33

Subspaces of Rn
Dimension and Rank 2.9 3,5,7,11,13,23,29
Introduction to Determinants
1,5,9,11,15,19,29,35 Exam 1

Properties of Determinants
3.2  1,5,7,11,19,23,29,31,35,41,43
Cramer's Rule 3.3 1,5,7,9,11,15,19,25 
Vector Spaces and Subspaces 4.1 1,5,7,11,15,21,31

Null Spaces, Column Spaces
Linearly Independent Sets: Bases 4.3 1,5,7,9,11,19,21,23,31
The Dimension of a Vector Space 4.5 1,7,11,17,21,22,29
Rank 4.6 1,5,11,19,21,29,31
Change of Basis 4.7 1,5,7,11,19
Applications to Difference Equations 4.8 1,5,7,11,19,23,31
Applications to Markov Chains 4.9 1,5,7,11,15,21

Eigenvectors and Eigenvalues
Exam 2 
The Characteristic Equation 5.2

Eigenvectors and Linear Transformations 5.4 5,7,11,17,19,31
Discrete Dynamical Systems 5.6 1,5,11,15
Inner Product, Length, and Orthogonality 6.1 1,5,17,23

Orthogonal Sets

Orthogonal Projections 6.3 1,5,7,11,15,17,19

The Gram-Schmidt Process
6.4 1,5,11,13,19

 Exam 3

Here is the set of Maple worksheets:

Maple worksheets for Mth 215

Maple worksheet on matrix exponential and systems of differential equations

Handout on matrix exponential and systems of differential equations

Here are some useful links for linear algebra: 

Jim Baglama's web page for MTH 215 with PDF of lectures

Linear Algebra Toolkit
S. Smith's Math 310 Home page
Math Archives - Linear & Matrix Algebra
STAT/MATH Center - Linear Algebra with Maple
Open Directory Project - Linear Algebra
Notes on Linear Algebra
Practice Linear Transformations