; 62182 INTRODUCTION TO LINEAR ALGEBRA
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# 62182 INTRODUCTION TO LINEAR ALGEBRA

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```									     62:182 INTRODUCTION TO LINEAR ALGEBRA
Course Outline                                   (MWF-slot 4) Winter 2008
Instructor:                Paola Di Muro (Room 1-75 Brodie) Phone: 727-7373
e-mail: dimuro@Brandonu.ca
website: http://flinflon.brandonu.ca/dimuro
Instructional Associate:   John Chen (Room 1-81 Brodie) Phone: 727-7410
Website: http://flinflon.brandonu.ca/chen
Recommended Text: Linear Algebra with applications by G. Williams, 6th ed., Jones    & Bartlett

Prerequisite:              Pre-Calc 40S or Math 40S or Applied Math 40S or equivalent or
62:090 or permission of Department
Course Material:
Systems of linear equations, Gauss-Jordan elimination, applications (1.1, 1.2, 1.6).
Matrices: operations and properties, inverse of a matrix (2.1, 2.2, 2.4).
Determinants, properties, Cramer’s rule, inverses method to solve SLE (3.1, 3.2, 3.3).
Introduction to vectors and operations with vectors, vectors in Rn (1.3, 1.4, 1.5, appendix A).
Vector spaces, linear combinations of vectors, linear dependence and independence,
subspaces of Rn, bases and dimension (4.1, 4.2, 4.3, 4.4, 4.5).
Linear transformations and their properties. Eigenvectors and eigenvalues (2.5, 2.6, 3.4).
Nullspace, rank and nullity. One to one and onto transformations (4.7, 4.8).
Lines and planes in R3. Imaginary and complex numbers (Appendix B, 2.3).
Other selected material and applications.
Course Goals:           Upon completion of this course, you should be able to:
- Recognize the solution set of a system of linear equations in 2 (or 3) variables as the set of
all points in common to the lines (planes) in the system.
- Solve systems of linear equations using matrices and row reduction.
- Add, subtract, multiply matrices, and find the inverse of a square matrix, if it exists.
- Evaluate the determinant of a square matrix, and use it to determine whether a matrix is
invertible.
- Add and subtract vectors geometrically and algebraically, and find a scalar multiple of
a vector.
- Use the dot product to find the angle between two vectors and the cross product to see
if two vectors are parallel.
- Recognize vector spaces, subspaces, determine vectors’ linear dependency /independency.
- Find the dimension and a set of basis vectors for a vector space.
- Find the rank of a matrix and bases for its row space and its column space.
- Recognize linear transformations and compose them.
- Find the equation of a plane and a line in R3,and determine the position of two lines in R3.

Academic dishonesty: the minimum penalty for any form of cheating on a test will be a
zero on that test. Academic disciplinary procedures may also be initiated, resulting in a record
assignment of a grade of “F – AD” for the course and suspension from the faculty.
It is a requirement for the course that everyone attends the weekly laboratory sessions, held
on Tuesdays 1:40-3:30pm (Theater A), starting from Tuesday, January 15. We will
write our tests and quizzes in the lab. You may work in a group on the lab quizzes or ask
the lab instructors for help. All tests and midterm are to be completed independently. You
are not allowed to use calculators for lab quizzes, tests, or exams. Cell phones and
electronic devices are NOT allowed in the room during tests and exams.
MARKING SCHEME

Tests & Times
Test 1                            Tuesday, Jan 29              8%
Midterm 1                         Tuesday, Feb 26              12 %
Test 2                            Tuesday, Mar 18              8%
Midterm 2                         Tuesday, Apr 1               14 %
Lab quizzes                       Jan 22, Feb 19, Mar 11,      8%
Apr 8,
Final Exam*                               Thurs., Apr 17               50 %
9 a. m. – 12 noon
*A final exam mark of under 45% is an automatic failure for the course.

Where to get help: - from John in room 1-81 during his office hours;
- from the lab assistant, during our lab periods on Tues, 1:40 – 3:30 pm (Th. A)
- from the Math Peer Tutors, located in room 102 in the McKenzie Bldg. The Peer
tutors will be on walk-in duty during hours that will be posted just outside room
102 and in the window of the Teaching Assistants’office (1-81 Brodie);
- from me, during my office hours, Mon from 1:00 to 3:00 pm, Tues from 10:30 to
11:00 am, Wed from 1:40 to 3:00 pm., Fri from 9:30 to 10:30 am, in room 1-75 BB;
call me if you need an appointment at a different time. I will be glad to help.

Rules for success: Aim at understanding the material, rather than memorizing it.
Math is the language of science. Make sure you understand the notation and are
capable of interpreting formulas.

Things to do: Attend class and lab regularly. I make an effort to present the material in
an understandable fashion, enriching it with significant examples.
Respect tests, midterms, and quizzes dates. If you are sick and miss a test or a quiz, contact
me (timely), providing a medical certificate.
The homework handouts represent only a focus paper. Make sure you expose yourself to more
practice questions from a textbook, from my website and/or Moodle. Check Moodle for
answer keys of homeworks and tests. Check the Library’s circulation desk for reserve material.

Study habits: Study daily, 6 to 9 hours each week are usually needed. Start from
studying your notes and reading the textbook. Make sure you reorganize the material into a
glossary, important results and how we use them in practice problems. Make sure you
focus on understanding what the problem is asking and relate it to how to achieve the
answer. Make sure you pause to interpret the result and check its reasonability.