THE UNIVERSITY OF WESTERN ONTARIO

LONDON CANADA

DEPARTMENT OF MATHEMATICS

__Mathematics 2120B: Intermediate Linear Algebra __

**Winter 2017**

**
**

**INSTRUCTOR:** Lex Renner, Professor, MC 130

**REQUIRED TEXTBOOK:** Linear Algebra, 4th Edition, by S. Friedberg, A. Insel and L. Spence,
published by Prentice Hall, ISBN: 0-13-008451-4.

**ANTIREQUISITES:** Mathematics 2211 A/B
**PREREQUISITES:** Mathematics 1600 A/B.

**COURSE OUTLINE:** Matrix operations, Gaussian elimination. Vector spaces: dimension, span and bases. Linear transformations and change of bases.

Determinants: their properties and how to compute them. Eigenvalues, eigenvectors, characteristic polynomial, diagonalization and Cayley-Hamilton Theorem.

This material is discussed in Chapters 1 - 5 of the text book. This course is more rigorous and less computational than Mathematics 1600 or 2211.

**EVALUATION OF STUDENT PERFORMANCE:**

Assignments, about six---worth 40%

Midterm --- 50 minutes, in class, on March 3 2017----worth 10%
**Final Exam --- worth 50%. Time: 7:00--10:00pm, April 9, 2017. Location: SSC 2024.**

Relevant Sections from the Text

Chapter 1: Sections 1.1 -- 1.6

Chapter 2: Sections 2.1 -- 2.5

Chapter 3: Sections 3.1 -- 3.4

Chapter 4: Sections 4.1 -- 4.4

Chapter 5: Section 5.1, Section 5.2, Theorem 5.23 and its Corollary.

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**ASSIGNMENTS**

**Assignment # 1:** Do all problems from here ** SCAN#1 **.
Due in class January 20 @ 12:30 pm.

**Assignment # 2:** Do the following problems: page 149 #5, 8, 9, 14; page 156 #4, 9; page 157 #16, 18. from here** SCAN#2 ** (all the circled problems).
Due in class February 3 @ 12:30 pm.

**Assignment # 3:** Do the following problems: page 228 #12, 13, 15, 18; page 252 #6; page 253 #10, 11. from here** SCAN#3 ** (all the circled problems).
Due in class March 1 @ 12:30 pm.

Answers are here:** ANSWERS#3 **

**Assignment # 4:** Do the following thirteen problems:

page 24 #42;

page 77 #16, 18;

page 78 #34b), 40;

page 128 #21, 22;

page 136 #32, 34;

page 219 #7, 22;

page 220 #27, 34.

These are the thirteen circled problems from here** SCAN#4 **.
Due in class March 24 @ 12:30 pm. Answers are here:** ANSWERS#4 **

**Assignment # 5:** Do the following four problems: #1d), 4b), 5, 6 from here
** SCAN#5 ** (all the circled problems). Due April 7, 2017 at 12:30.

**SUGGESTED PRACTICE PROBLEMS**

Section 1.3 (p19-23): #3, 5, 8b),d),f), 12, 20.

Section 1.4 (p33-35): 4b),d), 5d),f), 16.

Section 1.5 (p40-42): 2b),d),f), 7, 15, 18.

Section 1.6 (p54-58): 2b),d), 3b),d), 9, 14, 16, 24.

Section 2.1 (p74-76): 4, 5, 9b), 9e), 12, 17, 18.

Section 2.2 (p84-86): 2d), 4, 8, 16.

Section 2.3 (p96-98): 3, 9, 12, 16.

Section 2.4 (p106-108): 2, 3, 4, 5, 7, 17.

Section 3.1 (p151-152): 2, 3, 12.

Section 3.2 (p165-168): 2d), 2e), 2g), 3, 5e), 5f), 6b), 6f), 7.

Section 3.3 (p179-181): 2b), 2g), 3b). 3g), 4b), 7a), 7c), 10.

Section 3.4 (p194-198): 2c), 2f), 7, 10, 12.

Section 4.3 (p228): 2, 4, 6, 10, 16.

Section 4.4 (p236): 2b), 2d), 2h).

Section 5.1 (p256): 2b), 2c), 2d), 2f), 3b), 4c), 8a), 11c).

Section 5.2 (p279-281): 2, 3, 4, 12.

Section 5.4 (p323): 16, 17, 18.

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**IMPORTANT SENATE POLICY:**

Students are responsible for ensuring that their selection of courses is appropriate and accurately recorded and that all course prerequisites have been successfully completed. If the student does not have the requisites for a course, and does not have written special permission from his or her Dean to enroll in the course, the student may be removed from the course and it will be deleted from the student's record. This decision may not be appealed. A student will receive no adjustment to his or her fees in the event that he or she is dropped from a course for failing to have the necessary prerequisites.

**STATEMENT ON ACADEMIC OFFENCES:**

** **"Scholastic offences are taken seriously and students are directed to
read the appropriate policy, specifically, the definition of what
constitutes a Scholastic Offence, at the following Web site:
http://www.uwo.ca/univsec/handbook/appeals/scholoff.pdf** "**

**NEW MEDICAL EXCUSE REGULATIONS:**

If you are unable to meet a course requirement due to illness or other

serious circumstances, you must provide valid medical or other

supporting documentation to the Dean's Office as soon as possible and

contact your instructor immediately. It is the student's responsibility

to make alternative arrangements with their instructor once the

accommodation has been approved and the instructor has been informed. In the event of a missed final exam, a "Recommendation of Special Examination" form must be obtained from the Dean's Office immediately.

For further information please see:

http://www.uwo.ca/univsec/handbook/appeals/medical.pdf

A student requiring academic accommodation due to illness, should use the Student Medical Certificate when visiting an off-campus medical facility or request a Record's Release Form (located in the Dean's Office) for visits to Student Health Services.

The form can be found here:

https://studentservices.uwo.ca/secure/medical_document.pdf