Welcome to the Course Page of

SC/MATH  1025 3.0

Applied Linear Algebra

SU 2006


Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, Ontario  M3J 1P3

Course Organization:

Course Information
Course Schedule
Exams  Information
Links & Other Resources


This area will contain announcements and solutions to exams. Announcements made in class will be posted here in reverse chronological order and will not be repeated in class. Please take a minute to read the announcements carefully, as they often get updated. You may need to Reload/Refresh this page.
August 29: Please click  here  to see  your final exam mark and unofficial letter grade
  for the course. Also, please note that your official grade will be sent to you
  by the Registrar's Office upon the approval by the Senate.
August 14: Please note that I will be holding an additional office hour for last minute questions
  on Tuesday, August 15 from 3:00 to 4:00 PM.
August 01: Please note that Test #3 papers will be returned in the class on Wednesday,
  August 02.
  The Final Examination for the course will take place on Thursday, August 17
  from 9:00 to 12:00 PM in SLH B.
  Practice Problems Set for Chapter 7:
  Section 7.1:  1ab, 5, 6, 7, 8, 9, 10
  Section 7.2:  8 - 11, 18, 19, 20.
June 21: We will write Test #3 at the beginning of the lecture period on Wednesday,
  July 26th from 10:30 to 11:30  in two class rooms, as follows:
  - surname starting with A - K: CLH J
  - surname starting with L - Z: CLH H.
  On the test you will be responsible for all the material covered in class from
  Sections 3.3 -3.5, 4.1 - 4.3 and 5.1 of the text-book.
  Practice Problems Set for Chapter 5:
  Section 5.1:  1, 2, 8, 9, 10, 11, 12, 13, 14, 17, 18, 22
  Section 5.2:  1, 5, 7, 10, 11, 15, 19
  Section 5.3:  1, 2, 5, 7, 10, 11, 14, 15, 16.
June 12: Please note that the next two tutorials for the course will be held on
  Tuesdays, July 18 and July 25 from 12:30 to 1:30 PM in N501 Ross.
  The next week I will also be holding an office hour on Tuesday, July 18 
  from 4:00 to 5:00 PM instead of Wednesday, July 19.
  Practice Problems Set for Chapter 4:
  Section 4.1:  1, 3, 9, 10, 11, 15, 23
  Section 4.2:  1, 3, 5, 6, 7, 8
  Section 4.3:  2, 4, 8 - 14.
June 04: Please note that Test #2 papers will be returned in the class on Wednesday,
  July 05.
June 21: We will write Test #2 during the lecture period on Wednesday, June 28th
  from 10:30 to 11:30  in two class rooms, as follows:
  - surname starting with A - K: CLH J
  - surname starting with L - Z: CLH H.
  On the test you will be responsible for all the material covered in class from
  Sections 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, and 3.3 (up to orthogonal
  vectors (exclusive)) of the text-book.
  Practice Problems Set for Chapter 3:
  Section 3.1:  3 - 6. 9, 10, 15
  Section 3.2:  3, 4
  Section 3.3:  3, 4, 5, 6, 10, 12, 13, 16, 18, 19, 25
  Section 3.4:  2, 3, 4, 9, 10, 11, 17
  Section 3.5:  4, 5, 8, 13, 14, 20, 22, 23, 25, 30, 35, 39.
June 09: Practice Problems Set for Chapter 2:
  Section 2.1: 1 - 4, 10, 11, 17, 20, 22, 23, 25, 26, 29
  Section 2.2:  2, 3, 4 - 11, 12
  Section 2.3:  4, 5, 7, 8 - 11, 12, 15
  Section 2.4:  1(abc), 2(abc), 10, 11, 17.
June 05: Please note that Test #1 papers will be returned in the class on Wednesday,
  June 07.
May 26: Please note that there are no classes the next week. York University will
  be hosting The 2006 Congress of the Humanities and Social Sciences.
May 19: Practice Problems Set for Sections 1.4 and 1.5:
  1.4:  4, 7 - 11, 13 - 20, 23
  1.5:  1, 2, 6 - 8, 10, 13
  1.6:  1 - 20
  1.7:  1, 2(b), 3, 4, 5, 6, 7, 9, 10, 13, 15.
  We will write Test #1 during the lecture period on Wednesday, May 24th
  from 11:30 to 12:30  in two class rooms, as follows:
  - surname starting with A - K: CLH H
  - surname starting with L - Z: CLH J.
  On the test you will be responsible for all the material covered in class
  from Sections 1.1, 1.2, 1.3 and 1.4.
May 12: Practice Problems Set for Section 1.3:
  1 - 6, 11, 12, 13, 15 - 17, 20.
May 06: Please note that Tutorials for the course will start on Wednesday, May 10.
  As it was announced in the class on Wednesday, the tutorials will take place
  on Wednesdays from 14:00 to 15:00 in S105 Ross. Tutorials are optional.
  There is no need to register.
  Practice Problems Set for Sections 1.1 and 1.2:
  1.1:  1, 3, 6, 7, 8, 9, 11, 12
  1.2:  1, 2, 3, 4, 5, 6, 12, 13, 15, 16, 20, 22, 24, 26, 30, 31, 32.
 May 03: Welcome!
To view and/or print  PDF  files you need to download the free Acrobat Reader 

Course Information

Lectures: Days, Time and Room: Wednesday 10:30-13:30, CLH J
Instructor: Name: Dr. Iulduz Raguimov
  Office: S512 Ross Building
  Phone: x66092
  Office Hours: W 15:30-16:30, R 16:00-17:00, also by appointment
  Email: raguimov@mathstat.yorku.ca
Tutorials: Days, Time and Room: Wednesday 14:00-15:00, S105 Ross
TA: Name: TBA
  Email: TBA
Grading Three Class-Tests:  20% each
  Final Examination: 40%

Course Description: Topics include systems of linear equations, general matrix algebra, determinants, vector space concepts for Euclidean n-space (e.g., linear dependence and independence, basis, dimension, linear transformations, etc.), and an introduction to eigenvalues and eigenvectors. The course gives a one-term intensive introduction to linear algebra, with emphasis on its applications. It is particularly appropriate for students taking Science or Engineering programs which require one termís worth of linear algebra.
For a more detailed list of topics with references to the text-book, please see Course Schedule.


Elementary Linear Algebra -Applications Version, Ninth Edition

by Howard Anton and Chris Rorres, John Wiley & Sons, Inc. 2005
ISBN 0-471-66959-8.
Course Prerequisites: OAC Algebra and Geometry, or 12U Geometry and Discrete
Degree-credit AS/SC/AK/MATH 1021 3.0, or AS/SC/MATH 2021 3.0, 
Exclusions: or AS/SC/AK MATH 2221 3.0.
Important Dates: May 03: Classes commence.
May 12: Last date to enrol in the course without my permission.
May 19: Last date to enrol in the course with my permission.
July 04: Last date to drop the course without receiving a grade.
August 02: Last day of classes.
August 08-18: Examination period.

Course Schedule

(subject to any changes announced in class)




May 3 Introduction, 1.1, 1.2 Classes begin on Wednesday, May 03.
May 10 1.2, 1.3  
May 17 1.4, 1.5  
May 24 1.6, Test #1 Test #1 will take place on Wednesday, May 24.
May 31 No classes  
June 7  1.7, 2.1, 2.2  
June 14  2.3, 2.4, 3.1  
June 21  3.2, 3.3  
June 28 3.4, Test #2 Test #2 will take place on Wednesday, June 28.
July 5 3.5, 4.1  
July 12 4.2, 4.3  
July 19 5.1, 5.2, 5.3  
July 26 5.3, 7.1, Test #3 Test #3 will take place on Wednesday, July 26.
August 2 7.2, Review Classes end Wednesday, August 02.
August 8-18 Final Examination Thursday, August 17 from 9:00 to 12:00 PM in SLH B.


Throughout the term, the everyday homework assignment is to do as many of the problems from the text-book as you find necessary to develop your understanding of the course material. These will not be collected for grading and hence will not directly affect your grade. While these will not directly affect your grade, it is extremely important that you complete as many problems as possible. Do not memorize them. Rather, learn how to solve problems like them. There is nothing like a bit of computation to strengthen understanding in mathematics! Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! It is recommended to read the relevant sections of the text-book before every class. Next to the classes, working out the answers to the problems the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the text-book. I will regularly make specific suggestions concerning problems to do or to avoid. It is quite practical to work on your own or together in small groups. Each student should do at least two hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.

Exams Information

Lecture/Test Rules:

Please turn off all cell phones and pagers before entering the lecture hall. For tests and exam cell phones, digital dictionaries, palms, pagers, computers, and hats with large peaks are not allowed. All such devices as well as all books, papers, knapsacks, and briefcases must be left at the front of the lecture hall. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat are pens, pencils, student ID, a non-graphing, non-programmable calculator and purses.
You are responsible for all material covered in lectures.
You may not use graphing or programmable calculators on the tests and final exam. Photo identification and signing-in are required at all tests and exam.

Final Grade:

The composition of the final grade is as follows:
Three Class-Tests (60 minutes each written tests held in lecture period):   20% each  (Tentative dates for the tests: Wednesdays May 24,  June 28 and July 26).
Final Examination
(three-hour exam scheduled by the Registrar's Office):   40% of the overall grade, will take place on Thursday, August 17 from 9:00 to 12:00 PM in SLH B.
All test-marks you receive should be interpreted as raw scores and not "percentages". The statistics of scores will be announced for all tests. Cut-off for converting midterm scores into letter grades will be announced prior to the drop date. Students have seven days from the date of the return of a test paper to appeal their marks. Some test papers (randomly selected) are photocopied before they are handed back, so we can detect subsequent alterations. The lowest mark obtained on any class-test will be replaced by the mark on the final exam if the final exam mark is higher.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-ups will be done for the class-tests.  Missed tests will be counted as zero, except under extreme circumstances. If an acceptable reason, with appropriate documentation, is given for having missed test, the mark for that test will be determined by the final examination mark. What is an acceptable reason? A brief note from a doctor is not acceptable, because some doctors will write such notes without careful consideration. What is needed from the doctor is a detailed, typed and signed letter, indicating what the illness was, and also why that illness prevented the student from writing the test. I also may require a telephone conversation with the doctor to verify matters, so the student will have to give the doctor a permission to discuss the matter with me. At the same time, missing tests is extremely dangerous and not recommended. As experience has shown, students who miss class tests because of some 'mysterious illnesses' will usually average 30% on the final exam. A student who misses the final examination will be allowed to write a make-up exam only if both of the following conditions are met:
the student notifies me (raguimov@mathstat.yorku.ca) or the Department of   Mathematics and Statistics (Undergraduate Office, N502/N503 Ross Building, 416-736-2100 ext. 55902) in advance that the exam will be missed.
    2) the student provides a medical certificate showing a physical incapability of writing the exam within one week following the exam.
Students who miss the final examination and do not meet both conditions will receive a grade of F.
It is student's responsibility to fill out and submit the Deferred Standing Agreement Form.
Note: Do not make vacation/job plan until the final exam date is known: having a plane ticket for Las Vegas
or Hawaii on August 14 is NOT a legitimate excuse for absence from a final exam on August 17.

Religious Observance:

 York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for in-class tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first two weeks of classes. Please note that if the final exam date poses a conflict, students must complete the Final Exam Accommodation Form, which can be obtained from the Registrarís Office.

Academic Honesty:

Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of oneís programme or specialization may result in serious consequences. Refer to the Senate Policy on  Academic Honesty.


Individual questions can be discussed by e-mail, or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments nor HTML-formatted mail. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be up-dated regularly to include important announcements made in class, such as the material to be covered on the tests. E-mail notes requesting such information contained on the web page will be answered the last.

Links and Other Resources

1-  York Undergraduate Math Program
2-  Study Groups

Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca

© 2006, All Rights Reserved, York University & Iouldouz S. Raguimov

Last modified August 29, 2006