Welcome to the Course Page of

MATH 2022 3.00 M

Linear Algebra II

Summer 2013


Department of Mathematics and Statistics
Faculty of Science
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 21:

Please click here to see your final exam mark and unofficial letter grade


for the course. Also, please note that your official grade may be sent to


you by the Registrar's Office upon the approval by the faculty.



August 03:

As it was announced in the class on Thursday, the Final Examination for


the course will take place on Friday, August 09 from 19:00 to 22:00


in VH C. The exam will be comprehensive, covering the entire course


material according to theCourse Schedulebut with an emphasis on the


more recent material covered after the second test. If less common formulas


are needed on the exam, then those will be provided on the exam.


There will be several questions, some with a few parts. Marks for each


question will be indicated. You have to show all your work, and you


should explain your solutions where appropriate. Unofficial final grades


for the course will hopefully be posted to the course web page by


Wednesday, August 21. Please also note that I will be holding an


additional office hour for last minute questions on Tuesday, August 06


from 14:00 to 15:00.

July 31:

As it was announced in the class after the test yesterday, the graded Test #2


papers will hopefully be ready to pick up on Tuesday, August 6 at 2 PM.


I am making availablesolutionsto the test questions.

July 26:

As it was announced in the class yesterday, we will write Test #2 during the lecture


period from 18:00 to 19:20 on Tuesday, July 30 in S137 Ross. On the test you


will be responsible for the all material covered in class from Sections 6.3, 6.4,


7.1, 7.2, 7.3, 8.1, 8.4, 5.6 and 8.2 of the textbook.

July 22:

Practice exercises for Section 5.6, Chapters 8 and 9:


5.6:  # 1, 2(a,b,c), 4, 14;


8.1:  # 1, 2, 4, 13, 14, 16;


8.2:  # 1, 5, 7, 9, 13, 14, 16, 23, 25;


8.3:  # 1, 3, 7, 9;


8.4:  # 1, 2;


9.1:  # 1, 4, 5, 10.


Please note that the student course evaluations are available on-line


at the URL link  http://courseevaluations.yorku.ca  until August 05,


2013. It is the time for you to be the judge. Please go on-line and


complete the course evaluation.

July 16:

Practice exercises for Chapter 7:


7.1:  # 1, 2, 3, 4, 11, 14, 15;


7.2:  # 1, 2, 6, 8, 9, 10, 24, 28, 30;


7.3:  # 1, 4, 6, 10, 23.

July 11:

As it was announced after the test today, the graded Test #1 papers will hopefully


be returned in the class on Thursday, July 18. I am making availablesolutionsto


the test questions.

July 09:

As it was announced in the class today, we will write Test #1 during the lecture


period from 18:00 to 19:20 on Thursday, July 11 in S137 Ross. On the test you


will be responsible for all the material covered in class from Sections 5.1, 5.2,


5.3, 5.4, 5.5, 6.1, 6.2 and 6.3 of the textbook. Please note that no more than 25%


of the questions of the test will be from Sections 6.1, 6.2 and 6.3 of the textbook.


Also, please note that NO calculators, internet connected devises or any other aids


will be permitted on the test.

July 07:

Practice exercises for Chapter 6:


6.1:  # 1, 2, 4, 6, 12, 14;


6.2:  # 1, 2, 3, 5, 6, 8, 9, 13, 21, 27;


6.3:  # 1, 2, 3, 4, 10, 12, 15, 23, 27, 32, 33;


6.4:  # 1, 3, 7, 18, 23, 25, 26.

July 04:

According to the clarification that I received from the department yesterday,


we will be using the 6th Edition of the textbook this term. The 7th Edition of


the textbook will be used starting from Session 2013-2014. I apologise for the


inconvenience caused by this.

June 25:

I am making available Errata corrections to the 6th Edition of the textbook.

June 24:

Welcome back!


Practice exercises for Chapter 5:


5.1:  # 1, 2, 3, 5, 6, 12, 15, 16, 18, 23, 24;


5.2:  # 1, 4, 6, 7, 9, 18, 19, 20;


5.3:  # 4, 5, 6, 7, 13, 15, 18;


5.4:  # 1, 2, 3, 7, 11, 12, 14, 15;


5.5:  # 1, 2, 4, 5, 9, 16.


Please note that Tutorials for the course will be done in MathLab, S525 Ross


Building, which is open throughout the term: Monday-Thursday from 11:00 to


13:00 and from 15:00 to 17:00.

Course Information

MATH 2022:


Summer 2013






TR 18:00-21:00, S203 Ross



Iulduz Raguimov



S512 Ross



416-736-2100, EXT 66092 or 416-736-5250


Office Hours:

MR 16:00-17:00, also by appointment





Two Tests: 



Final Examination:


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, orthogonality, eigenvalues, diagonalization, least squares and quadratic forms. Similar to AS/SC/AK/MATH 2222 3.00 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 textbook, please see Course Schedule.


Linear Algebra with Applications, Seventh Edition

by W. Keith Nicholson

McGraw-Hill Ryerson, 2013. ISBN 0-07-040109-9

Course Prerequisites:

AK/AS/SC/MATH 1021 3.00 or AS/SC/MATH 2021 3.00.


If you have not taken MATH 1021 3.00, it is essential that you take it first and then take

MATH 2022.

Course Credit



 AS/SC/AK/MATH 2222 3.00.


Important Dates:

June 25: Classes commence.

June 28: The last date to enrol in the course without my permission.

July 05: The last date to enrol in the course with my permission.


July 11: Test #1

July 19: The last date to drop the course without receiving a final grade.


July 30: Test #2


August 01: The last day of classes.

August 06-16: Examination period.

Course Schedule

(subject to any changes announced in class)

WEEK of:



June 24 

Introduction, 5.1, 5.2

Classes begin on Tuesday, June 25.

July 01 

5.4, 5.5, 5.3


July 08

6.1-6.3, Test #1

Test #1 will take place on Thursday, July 11.

July 15 

6.4, 7.1-7.3


July 22

8.1, 8.4, 5.6, 8.2

July 29

Test #2, 8.3, 9.1, 8.8

Test #2 will take place on Tuesday, July 30.
The classes end on Thursday, August 01.

August 06-16

Final Examination

Friday, August 09.

Note: The course will not cover all the sections of each chapter from the textbook.


Throughout the term, practice exercises will be posted to the Announcements section. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence will not directly affect your grade. However, it is extremely important that you complete all assigned exercises. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. 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 textbook before every class. Next to the classes, working out the answers to the problems is 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 textbook. 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/Exam Rules:

Please turn off all cell phones and pagers before entering the lecture hall. For tests and exam cell phones, calculators, digital dictionaries, palms, pagers or any other internet connected 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 official grades at York University are LETTER grades. Qualitative descriptions of these grades can be found in the York Calendar at this link. Your test marks will be on a numerical scale because these have to be weighted and averaged in various ways, but THERE IS NO AUTOMATIC PREDETERMINED CORRELATION BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the "numerical" grades you receive are NOT to be interpreted as percentages; they are merely 'raw scores'. When the tests are returned in class, the distribution of 'raw scores' will be announced along with an approximate conversion to letter grades. The median letter grade for the course will likely fall between C and C+.
The composition of the final grade is as follows:
Two Tests (80 minutes each written tests held in lecture periods)††† :30% + 20% (Tentative dates for the tests: Thursday, July 11 and Tuesday, July 30). Final Examination:50% of the overall grade, will take place during the examination period between August 06 and 16, 2013.
Students have five days from the date of the return of test papers to appeal their marks. Some test papers (randomly selected) are photocopied before they are handed back, so we can detect subsequent alterations. Once you have written both tests and your final exam grade is higher than your average test grade, your final exam will be counted as 60% and each test as 20% of your overall grade for the course.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-up will be done for the tests. A missed test will be counted as zero, except under extreme circumstances in which case the corresponding percentage of the overall grade will be "forwarded" to the final exam. If you miss a term-test  for medical reasons you must turn in  within one week following the test date the Attending Physician's Statement form provided  here after getting it filled in by your doctor. No other type of medical note will be accepted.  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 Department of Mathematics and Statistics (Undergraduate Office, N502/503 Ross Building, 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed;
  2) the student submits within one week following the exam date the Attending Physician's Statement form provided  here after getting it filled in by his/her doctor .
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 to Banff or Hawaii for August 10  is NOT a legitimate excuse for absence from a final exam on August 14.

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:

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.  Photo identification and signing-in are required at all tests and exam. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.


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-  Online Forum
2-  York Undergraduate Mathematics Program
3-  Links to Linear Algebra sites
4-  How To Write Proofs
5- Local time in Toronto

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

© 2004-2013, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated August 21, 2013