Welcome to the Course Page of

AK/MATH 2022 3.0 A

Linear Algebra II

Summer 2005


School of Analytic Studies and Information Technology
Atkinson Faculty of Liberal and Professional Studies
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 tests. 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 25: Please click  here  to see  your final exam mark and unofficial letter grade
  for the course.
  Please note that Deferred Final Examination will take place on Friday,
  September 09 from 13:30 to 16:30 in TEL 0011.
August 05: I am making available  solutions  to Test #3 in PDF format. You may pick up
  your test paper from the box outside of my office (S512 Ross).
  Please click to check your  term grades.  Please note that Test #3 grades were
  curved up for 2 points. If you find any discrepancy, please send me an e-mail
  and come to see me before the final examination with your test papers.
July 26: Please note that we will write Test #3 on Thursday, July 28 from 6:00 to 7:00pm
  in VH D. On the test you will be responsible for the material covered in class
  from Sections 7.2, 7.3, 7.4, 7.7, 7.8, 8.1 and 8.2 of the text-book.
July 25: I will bring the course evaluation forms to the class on Tuesday, July 26th.
  It is the time for you to be the judge. Please come and fill out the evaluation
July 22: Please note that Test #2 papers were returned in the class on Thursday.
  If you did not pick up your test paper, you may pick it up together with the
  solutions to the test questions during office hours.
July 12: Please note that we will write Test #2 on Thursday, July 14 from 6:00 to 7:00pm
  in CLH C. On the test you will be responsible for the material covered in class
  from Sections 6.1, 6.2, 6.3, 6.4 and 7.1 of the text-book.
July 11: Please note that Test #1 papers will be returned during the class on Tuesday,
  July 11. I am making available  solutions  to the test questions in PDF format.
June 29: Please note that we will write Test #1 on Tuesday, July 05 from 6:00 to 7:00pm
  in CLH K. On the test you will be responsible for the material covered in class
  from Sections 5.1, 5.2, 5.3 and 5.4 of the text-book.
 June 27: Please note that effective Tuesday, June 28 the lecture and tutorial room will
  be changed to the room S171 Ross.
 June 21: Welcome back!
To view and/or print  PDF  files you need to download the Acrobat Reader 

Course Information

Course: Session: 2005 Summer
  Section: A
  Lectures: TR 6:00-9:00pm, S171 Ross
Instructor: Name: Iulduz Raguimov
  Office: S512 Ross
  Phone: 416-736-5250, Ext.66092
  Office Hours: MW 5:30-6:30pm, R 4:00-5:00pm, also by appointment
  E-mail: raguimov@mathstat.yorku.ca  
  Tutorials: TR 5:00-6:00pm, S171 Ross
Tutorial Leader: Name: Ziting Zeng
  E-mail: ziting@mathstat.yorku.ca
Grading: Three Class Tests  20% each
  Final Examination 40%

Course Description:  This course is required in Specialized Honours Statistics and all Applied Mathematics, Mathematics and Mathematics for Commerce programs except the BA program in Mathematics for Commerce. Topics include inner product spaces, linear transformations, eigenvalues, diagonalization, least squares, quadratic forms and Markov chains. Similar to AS/SC/AK/MATH 2222 3.0 but at a more advanced level. Additional topics: General linear transformations, matrix of a linear transformation from V to W relative to bases for V and W, effect of a change of bases. For a more detailed list of topics with references to the text-book, please see Course Schedule.


Linear Algebra with Applications, Fourth Edition

by W. Keith Nicholson
McGraw-Hill Ryerson, 2003. ISBN 0-07-088046-8
Course Prerequisites: AK/AS/SC/MATH 1021 3.0 or AS/SC/MATH 2021 3.0 or permission of the instructor.
  If you have not taken MATH 1021, it is essential that you take it first and then take
MATH 2022.
Degree-credit AS/SC/AK/MATH 2222 3.0.
Important Dates: June 21: Classes commence.
June 30: The last date to enrol in the course without my permission.
  July 01: Canada Day (The University is closed). 
July 08: The last date to enrol in the course with my permission.
July 15: The last date to drop the course without receiving a final grade.
  July 28: The last day of classes.
August 01: Civic Holiday (The University is closed).
August 02-12: Examination period.

Course Schedule

(subject to any changes announced in class)




June 20-24   Introduction, 5.1, 5.2, 5.3 Classes begin on Tuesday, June 21.
June 27-July 01  5.4, 6.1, 6.2, 6.3 Tutorials begin on Tuesday, June 28.
July 04-08  6.4, 7.1, 7.2, Test #1 Test #1 will take place on Tuesday, July 05.
July 11-15  7.3, 7.4, 7.7, Test #2 Test #2 will take place on Thursday, July 14.
July 18-22 7.8, 8.1, 8.2, 8.3  
July 25-29   8.4, 8.5, 9.1, Test #3 Test #3 will take place on Thursday, July 28.
The classes end on Thursday, July 28.
August 02-12 Final Examination Thursday, August 11 from 19:00 to 22:00 in CLH G.

Note: The course will not cover all the sections of each chapter from the text-book.


Chapter 5: Section 5.1 Exercises: 1, 2, 3, 5, 7, 8, 15, 17, 24, 29
  Section 5.2 Exercises: 1, 2 , 3, 7, 13, 16
  Section 5.3 Exercises: 1, 2, 4, 5, 9, 16
  Section 5.4 Exercises: 1, 2, 4, 9, 11, 14, 23
  Suppl. Exerc. Exercise: 1
Chapter 6:  Section 6.1 Exercises: 1, 2, 4, 6, 12, 14
  Section 6.2 Exercises: 1, 2, 3, 5, 6, 8, 9, 13, 21, 27
  Section 6.3 Exercises: 1, 2, 3, 4, 10, 12, 15, 18, 21, 23, 37
  Section 6.4 Exercises: 1, 3, 7, 17, 20, 22, 23
  Suppl. Exerc. Exercise: 2
Chapter 7: Section 7.1 Exercises: 4, 5, 8, 9, 11, 14, 16, 28, 30
  Section 7.2 Exercises: 1, 5, 7, 9, 13, 15, 16, 22, 24
  Section 7.3 Exercises: 1, 3, 7, 9
  Section 7.4 Exercise: 1
  Section 7.7 Exercises:  1, 2, 3, 7
  Section 7.8 Exercises:  1, 2, 7
Chapter 8: Section 8.1 Exercises: 1, 2, 3, 4, 11, 14, 15
  Section 8.2 Exercises: 1, 2, 6, 8, 9, 10, 24
  Section 8.3 Exercises: 1, 4, 6, 10, 23
  Section 8.4 Exercises: 1, 4, 5, 10
  Section 8.5 Exercises: 1, 3, 6, 8, 9, 10, 13
Chapter 9: Section 9.1 Exercises: 1, 3, 4, 5, 10, 12, 13, 16, 22, 32
  Section 9.2 Exercises: 1, 2, 3, 6, 7, 10, 12, 21, 22
  Section 9.3 Exercises: 1, 2, 5
  Section 9.4 Exercises: 2, 3, 6, 8, 11, 14, 15
  Section 9.5 Exercises: 1, 4

The homework assignments are posted but solutions will not be collected for grading. While these will not directly affect your grade, it is extremely important that you complete all of the assigned homework. 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 exercises (the back of the text-book contains the answers to the most of them) is the most important preparation for the tests and exam that will contain for the most part but not exclusively, very similar questions. 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 the exercises.

Exams Information

Lecture/Exam Rules:

Please turn off all cell phones and pagers before entering the lecture hall. For tests and exam cell phones, digital dictionaries, palms, pagers or other electronic devices 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 and purses.
You are responsible for all material covered in lectures.
Note: 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 periods):   20% each (Dates for the tests: Tuesday, July 05 and Thursdays, July 14 and July 28, 2005).
Final Examination
:   40% of the overall grade, will take place on Thursday, August 11 from 19:00 to 22:00 in CLH G.
All test marks you receive should be interpreted as raw scores and not "percentages". The statistics of scores will be announced for all tests. Students have seven days from the date of the return of a test paper to appeal their marks. Cut-off for converting midterm scores into letter grades will be announced prior to the drop date.

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 in-class tests.  Missed tests will be counted as zero, except under extreme circumstances. If you miss a class test  and provide a medical certificate showing a physical incapability of writing it, the corresponding percentage of the final grade will be "forwarded" to the final exam. However, 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:
1) the student notifies me (raguimov@mathstat.yorku.ca) or the School of Analytic Studies & Information Technology (Mathematics Department, Room 2005, TEL Building, Tel: 416-736-2100, Ext. 33203; Fax: 416-736-5188) 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 Hawaii or Las Vegas on
August 05 is NOT a legitimate excuse for absence from a final exam on August 10.

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) by June 28. 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:

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-  Study Groups
2-  York Undergraduate Mathematics Program
3 School of Analytic Studies & Information Technology
4-  Links to Linear Algebra sites

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

© 2005, All Rights Reserved, York University & Iouldouz S. Raguimov

Last modified August 25, 2005