Welcome to the Course Page of

MATH 1021 3.00 A

Linear Algebra I

Winter 2014-15


Department of Mathematics and Statistics
Faculty of Science and Engineering
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.

May 06:

Please  click here  to see your final exam mark and unofficial


letter grade for the course. Please also note that your official


grade for the course will be available by the Registrar's


Office upon the faculty approval.



April 16:

Please note that the Final Examination for the course will take place on


Saturday, April 25, 2015 from 9:00 AM to 12 PM in ACW 006.


The exam will be comprehensive, covering the entire course material


covered in class according to the Course Schedule with an emphasis on


the more resent material covered after Test #2. If less common formulas


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


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 should


explain your solutions where appropriate. Unofficial final grades for the


course will hopefully be posted to the course web page by May 08, 2015.


I will be holding an additional office hour on Monday, April 20 from


12:00 to 1:00 PM to answer your questions.


Please also note that the Math Lab is open according to the schedule:



April 14:

Please note that the graded Test #2 papers will be returned in the class on


Thursday, April 16. I am making available  solutions  to the test questions


in PDF format.

April 10:

Practice exercises for Chapter 4:


Section 4.1:  # 3, 4, 5, 7, 8, 11, 14, 20, 21, 22, 23(b), 24, 33, 34;


Section 4.2:  # 2, 3, 4, 7, 9, 11, 12, 13, 14, 15, 16, 19, 20, 24, 32, 34, 41;


Section 4.3:  # 2, 3, 4, 5, 7, 8, 11, 13, 16, 17, 18.

April 03:

Please note that the student course evaluations are available at the URL link:




until Friday, April 17, 2015. It is the time for you to be the judge. Please go


on-line and complete the course evaluation. Thank you!

April 01:

Please note that we will write Test #2 during the lecture period on Tuesday,


April 07 in the two class rooms as follows:


- family name starting with A - K: CLH J;


- family name starting with L - Z: S137 Ross.


On the test you will be responsible for all the material covered in class from


Sections 2.6, 2.7, 3.1, 3.2 and 3.3 of the textbook.

March 27:

Please note that this week we have finished covering in class the Cofactor Expansion,


pages 130-134 of the textbook up to Theorem 4 (inclusive). Then we have started


Determinants and Matrix Inverses. On the Thursday’s class we have finished covering


the material from pages 137-144 of the textbook up to the Polynomial Interpolation


(exclusive). On the next Tuesday’s class I will be doing few more exercises from


Section 3.2 and start Section 3.3 Diagonalization and Eigenvalues. Please try to solve


all the assigned practice exercises from Sections 3.1 and 3.2 of the textbook.

March 21:

As it was announced in the class Thursday, the classes will end on Friday, April 17.


Please click here to see a modified course schedule.


On the Tuesday, March 17th class we have covered the material from the pages


103-107 of the textbook. On the Thursday, March 19th class we have covered the


material from the pages 126-130 of the textbook up to Theorem 2 (exclusive).


Practice exercises for Chapter 3:


Section 3.1:  # 1, 4, 5, 6, 7, 9, 10, 11, 13, 14, 17, 27;


Section 3.2:  # 1, 2, 3, 5, 8, 9, 10, 15, 16, 20, 25, 28;


Section 3.3:  # 1, 2, 3, 7, 8, 9, 10, 12, 13, 15, 17, 24, 26, 27;


Section 3.4:  # 1.

March 16:

Please note that the classes will resume shortly. Click the link below for the details:



March 03:

Last night, in a very large membership meeting, all three units of CUPE 3903 voted


not to send the employer's final offer to a formal ratification vote. Overall, the vote was


70% against sending the offer to ratification vote. The union executive then decided


to call the strike, given that it had a strike mandate in hand from earlier in February.


That means that, as of Tuesday March 03 at 12:01am, CUPE 3903 is on strike.


The University’s Senate Executive decided on February 27, 2015 that all academic


activities, including classes are cancelled until the strike is settled. Unfortunately,


at this point there is no way to know how long the strike might last. In the meantime,


even though it is difficult, I strongly recommend that you take this opportunity to review


course material covered up to now, catch up with readings if you've fallen behind, and


even read ahead, and continue to work on your assignments. Although due dates are


frozen, course work will be due when we return to classes. Keeping up with work will


make the transition back to classes a little less shocking.


Please distribute this message to your class mates. Thank you.

March 02:

As it was promised in the last class, I am making solutions to the questions


of White and Green versions of Test #1.


Also, please click here to see your score for Test #1.

February 28:

Please note that the Department of Mathematics and Statistics will be hosting


Science@50 anniversary event on Tuesday afternoon. The event will include


several short and informal lectures about cool Math in Simpsons cartoon,


followed by pizza and a career panel (a discussion with our alumni about


possible career paths in Math). The students who are interested to attend


this event should register at this website:




You can also find all information about the event at this website.

February 08:

As it was announced in the class on Thursday, we will write Test #1


during the lecture period on Thursday, February 12 in the two class


rooms as follows:


- family name starting with A - K: CLH J;


- family name starting with L - Z: CLH K.


On the test you will be responsible for all the material covered in class


from Sections 1.1, 1.2, 1.3, 1.6, 2.1, 2.2, 2.3, 2.4 and 2.5 (inclusive) of


the textbook according to the Course Schedule.

January 24:

Tutorials for the course are taking place in the MathLab, S525 Ross Building,


which is open throughout the term: Monday-Friday from 10:30 AM to 3:30 PM.


For more information on the MathLab please check the web page at:




Practice exercises for Chapter 2:


Section 2.1:  # 1, 2, 4, 6, 10, 13, 14, 15, 19, 20;


Section 2.2:  # 1, 2, 3, 5, 7, 8, 10, 11, 16, 17, 20;


Section 2.3:  # 1, 2, 3, 4, 5, 8, 9, 12, 17, 22, 27, 30, 33, 34;


Section 2.4:  # 2, 3, 4, 5, 6, 8, 9, 10, 17, 20, 28, 36;


Section 2.5:  # 1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 17, 18;


Section 2.6:  # 1, 2, 3, 4, 6, 7, 8, 12, 18, 19, 22, 24;


Section 2.7:  # 1, 4.

January 21:

According to the requests of some students, I am making available the URL






As it was announced in class, in order to use eBOOK with STUDY & TESTING


PROGRAM you have to purchase the CONNECT Access Code. ISBN for the code


is 978-0-07-109419-7. You may purchase it from York Lane Bookstore or on-line.

January 12:

I am making available Errata Corrections to the 7th Edition of the textbook.

January 03:

Welcome back!


To view and/or print  PDF  files you need to download the Acrobat Reader 


Practice exercises for Chapter 1:


Section 1.1: # 3, 7, 8, 9, 10, 11, 13, 14, 15;


Section 1.2: # 2, 3, 5, 7, 9, 11, 12, 13, 15, 16;


Section 1.3: # 1, 2, 3, 5, 6, 7, 8, 9;


Section 1.6: # 2, 4;


Supplementary Exercises: # 1, 2, 3, 6, 13.


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

Course Information

MATH 1021:


Winter 2014-2015






T/R 14:30-15:50, CLH J



Iulduz Raguimov



S512 Ross



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


Office Hours:

MF 12:00-13:00 and T 16:00-17:00, also by appointment








Two Tests: 

25+20% each


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 linear equations, matrices, Gaussian elimination, determinants and vector spaces. Similar to SC/MATH 2221 3.00 but at a more advanced level. Additional topics: Euclidian n-spaces, lines and planes, linear transformations from R^n to R^m, rank and nullity of a matrix. 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, ISBN 978-0-07-040109-9

Optional Aids:



McGraw-Hill Ryerson, ISBN 978-0-07-109419-7


For more information on the latest technology and Learning Solutions


offered by McGraw-Hill Ryerson, please click the link:




Course Prerequisite:

One 12U or OAC mathematics course or equivalent.


Course Credit

SC/MATH 1025 3.00, SC/MATH 2021 3.00, SC/MATH 2221 3.00,


GL/MATH/MODR 2650 3.00.


Important Dates:

January 05: Classes commence.

January 19: The last date to enrol in the course without my permission.

January 30: The last date to enrol in the course with my permission.


February 12: Test #1


April 07: Test #2

April 17: The last date to drop the course without receiving a final grade.


April 17: The last day of classes.

April 19-28: Examination period.

Course Schedule

(subject to any changes announced in class)

WEEK of:



Jan 05-09

Introduction, 1.1

Classes begin on Tuesday, January 06.

Jan 12-16

1.2, 1.3


Jan 19-23

1.6, 2.1


Jan 26-30

2.2, 2.3


Feb 02-06

2.4, 2.5


Feb 09-13

2.6, Test #1

Test #1 will take place on Thursday, February 12.

Feb 16-20

No Classes

Reading Week.

Feb 23-27

2.6, 2.7


Mar 02-06


Mar 09-13


Mar 16-20

2.7, 3.1


Mar 23-27

3.2, 3.3

Mar 30-Apr 03

3.3, 3.4,


April 06-10

Test #2, 4.1, 4.2

Test #2 will take place on Tuesday, April 07.

April 13-17

4.2, 4.3, Review

The classes will end on Friday, April 17.

April 19-28

Final Examination


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


Throughout the term, recommended practice exercises will be posted to the Announcements section. In order to develop your understanding of the course material you must do all assigned exercises. 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! 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 exercises 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 exercises.

Exams Information

Lecture/Exam Rules:

All internet connected and other distractive electronic devices (cell phones, pagers, head phones, digital dictionaries, CD players, laptops) need to be turned off during class, i.e. during lectures, tutorials, tests and exams. All such devices as well as all books, papers, knapsacks, and briefcases must be left at the front of a lecture hall during tests and exams. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat during exams and tests are pens, pencils, eraser student ID and purses. Notes need to be taken manually; use of cellphone cameras in class is not allowed. 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 AUTOMATICPREDETERMINED 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): 25% + 20% (Tentative dates for the tests: Thursday, February 12 and Tuesday, April 07, 2015);
Final Examination 
(three-hour exam scheduled by the Registar's Office): 55% of the overall grade, will take place in April 2015, during the examination period.
Note: 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. Also, to encourage good exam performance: 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 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.
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, N502/503 Ross Building, 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed;
 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 for Banff or Hawaii on April 18 is NOT a legitimate excuse for absence from a final exam on April 23.

Religious Observance and Accessibility:

Special needs students, please identify yourselves to the course instructor as soon as possible. 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 examinamtion date poses a conflict, students must complete the Final Exam Accommodation form, which can be obtained from the Registrar’s Office. 
Please refer to appropriate Senate documents on:
  1) Course requirement accommodations for students with disabilities, including physical, medical, systematic learning and psychiatric disabilities;
  2) Student Conduct Standards.
Note that York University welcomes feedback on accessibility issues. Your feedback may be provided by sending an e-mail to: mathstat@yorku.ca

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 one’s programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty. Photo identification and signing-in are required at the all tests and exam.


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 or HTML-formatted e-mail. No texting, please. 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 Mathematics Program
2-  Study Groups
How To Write Proofs
4-  Local time in Toronto

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

© 2004-2015, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated May 06, 2015