Campus:Ohio University, Athens Campus
Academic Year:2014 - 2015
Term:Spring Semester
Course:MATH 3210 and MATH 5210
Title:Linear Algebra
Instructor:Mark Barsamian
Contact Information:My contact information is posted on my web page.
Office Hours:My office hours are posted on my web page.

This Course is Cross-Listed

Class Meets: Monday, Wednesday, Friday 10:45am - 11:40am in Morton 215

Course Description: A course in linear algebra for students majoring or minoring in the mathematical sciences. The course will introduce both the practical and theoretical aspects of linear algebra and students will be expected to complete both computational and proof-oriented exercises. Topic covered will include:

Prerequisites: 2302 Calculus II and (3050 Discrete Math or CS 3000) WARNING: No credit for both this course and MATH 3200/5200 (always deduct credit for first course taken)

Paper Syllabus The syllabus handed out on the first day of class can be obtained at the following link: (syllabus) The information on the paper syllabus is the same as the information on this web page.

Textbook Information
Title:Linear Algebra, 2014 Edition click on the book to see a larger image
click to enlarge
Author:Jim Hefferon
Publisher:Orthogonal Publishing
Price:roughly $20 for the paperback version at
Links: Author's web page for the book: (Link)
Free online PDF of the book: (Link) (You still have to buy a paperback copy for our class!)
Free online PDF of the solutions manual: (Link)

Online Math Software and Resources: (Link)

Grading: During the semester, you will accumulate points:

Homework Sets (10 Sets, 10 points each):100 points possible
In-Class Exams (4 exams, 150 points each):600 points possible
Comprehensive Final Exam:300 points possible
Total:1000 points possible

At the end of the semester, your Total will be converted to your Course Grade:

Total ScorePercentageGradeInterpretation
900 - 100090% - 100%AYou mastered all concepts, with no significant gaps
850 - 89985% - 89.9%A-
800 - 84980% - 84.9%B+You mastered all essential concepts and many advanced concepts, but have some significant gaps.
750 - 79975% -79.9%B
700 - 74970% - 74.9%B-
650 - 69965% - 69.9%C+You mastered most essential concepts and some advanced concepts, but have many significant gaps.
600 - 64960% - 64.9%C
550 - 59955% - 59.9%C-
400 - 43940% - 54.9%DYou mastered some essential concepts.
0 - 3990% - 39.9%FYou did not master essential concepts.

Note that although this grading scale may look easy compared to the usual 90,80,70,60 scale, it is actually not easier. The reasons are:

Course Structure: One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways:

Attendance Policy: Attendance is required for all lectures and exams, and will be recorded by a sign-in system.

Missing Class: If you miss a class for any reason, it is your responsibility to copy someone’s notes and study them. I will not use office hours to teach topics discussed in class to students who were absent.

Missing an Exam Because of Illness: If you are too sick to take an exam, then you must

  1. send me an e-mail before the exam, telling me that you are going to miss it because of illness,
  2. then go to the Hudson Student Health Center.
  3. Later, you will need to bring me documentation from Hudson showing that you were treated there.
Without those three things, you will not be given a make-up exam.

Missing Exams Because of a University Activity: If you have a University Activity that conflicts with one of our exams, you must contact me before the exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss an exam because of a University Activity without notifying me in advance, you will not be given a make-up exam.

Late Homework Policy: Homework is due at the start of class on the due date. Late homework is not accepted.

Collaborating on Homework: You are encouraged to work together on the homework. If you work in a productive way with other students, you will probably learn the math better. You will certainly learn valuable communication skills. But collaborating does not mean copying. You may figure out problems and arrive at solutions together, but the words you write and turn in should be your own. If two or three or five students work together, the result should be a higher quality of work, with fewer errors. When I grade homework, if I find identical wording, identical math, and identical mistakes in different students’ papers, I will deduct points. If this happens, it is not meant to be a punitive measure, and I do not mean for you to think that I am accusing you of cheating. But I do mean for it to be feedback that tells you that you are not really collaborating and that you are not doing good work. Collaborating is a skill that requires practice.

Cheating on Exams: If cheat on an exam, you will receive a zero on that exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR). If you cheat on another exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.

Special Needs: If you have a physical, psychiatric, or learning disability that requires accommodation, please let me know as soon as possible so that your needs may be appropriately met.

Suggested Exercises: The goal of the course is for you to be able to solve the 233 exercises on this list. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study. Note that the solutions to all of the textbook exercises are available free online.

ChapterSectionSubsectionSuggested ExercisesPages
OneI118, 20, 23, 29, 30, 32, 33, 35pages 9 - 12
OneI218, 20, 21, 22, 23, 24, 26, 27, 30pages 19 - 22
OneI314, 16, 17, 19, 20pages 32 - 33
OneIII18, 9, 10, 12pages 54 - 55
OneIII210, 16, 18, 19pages 62 - 63
TwoI119, 20, 21, 22, 24, 29, 32, 35, 36, 37, 38pages 86 - 90
TwoI220, 21, 22, 26, 27, 28, 29, 31, 32, 40, 44pages 97 - 101
TwoII120, 21, 24, 27, 28, 29, 30, 35, 42acpages 110 - 114
TwoIII118, 19, 20, 22, 23, 24, 28, 29, 31, 35, 37, 38pages 118 - 120
TwoIII219, 20, 25, 26, 27, 31, 33pages 125 - 126
TwoIII319, 20, 21, 25, 26, 27, 29, 37, 38, 40pages 132 - 134
ThreeChapter 3 problems and page numbers shown are from the new edition of the book. The problem numbers and page numbers in (parentheses) are from the old edition of the book
ThreeI113, 17(15), 18(16), 20(18), 23(21), 24(22), 29(27), 32(30), 33(31), 37(35)pages 172 - 175
ThreeI210, 15, 17, 20pages 179-180 (181–182)
ThreeII118, 19, 20, 21, 24(23), 25(24), 27(26), (31)30, 32(31), 35(34), 40(39), 42(41), 42(42)pages 186-189 (188-191)
ThreeII221, 22, 25(23), 26(24), 28(26), 33(31), 35(33), 38(36)pages 198-201 (200-202)
ThreeIII112, 13, 14, 15, 16, 18(17), 19(18), 20(19), 21(20), 22(21), 24(23), 29(28)pages 209-212 (210-213)
ThreeIII212, 16, 22(20), 23(21), 24(22), 25(23), 28(26)pages 218-220 (218-221)
ThreeIV18, 12, 14, 15, 16pages 223-224 (224-226)
ThreeIV214, 17, 21(20), 26(25), 27(26), 32(31), 34(33), 35(34)pages 230-233 (231-234)
ThreeIV324, 26, 29, 31(NA), 32(37), 33(NA), 34(31), 35(32), 36(33), 39(36), 43(41), 44(42)pages 240-243 (241-243)
ThreeIV415, 17, 18, 20, 21, 26, 27, 30pages 249-250 (249-251)
ThreeV18, 11, 12, 15, 18pages 254-256 (255-256)
ThreeV212, 14(NA), 17(15)pages 261-263 (262-263)
FourI13, 5, 6, 8, 9 (a ≠ 0 and ae-bd ≠ 0), 16, 17pages 319 – 321
FourI29, 12, 13, 14, 15, 16, 19pages 324 – 326
FourI317, 20, 21, 26, 28, 33pages 333 – 335
FourIII111, 12, 14, 15, 18, 21, 23, 24pages 355 - 356
FiveII14, 6, 7, 11, 18 pages 387 - 388
FiveII27, 8, 9, 10, 11, 14, 15, 17, 18pages 392 - 393
FiveII320, 21, 23, 25, 27, 28, 31, 33, 40pages 400 - 402

Homework Assignments to Turn In: These homework sets will be collected, graded, and returned to you. Staple the cover sheet to the front of your work.

AssignmentDue DateCover SheetSolutionsSupplemental Materials
H1Fri Jan 16H1 Cover SheetH1 Solutions 
H2Wed Jan 28H2 Cover SheetH2 Solutions 
H3Mon Feb 9H3 Cover SheetH3 Solutions 
H4Mon Feb 16H4 Cover SheetH4 Solutions 
H5Mon Mar 9H5 Cover SheetH5 SolutionsNotes on Images, Preimages, and Inverse Functions
H6Wed Mar 11H6 Cover SheetH6 Solutions 
H7Wed Mar 18H7 Cover SheetH7 Solutions 
H8Wed Apr 1H8 Cover SheetH8 Solutions 
H9Fri Apr 10H9 Cover SheetH9 Solutions 
H8Wed Apr 22H10 Cover SheetH10 Solutions 

Remark on Errors in the Homework Solutions: The homework solutions that I write are bound to contain mistakes. If you find a mistake in one of the printed homework solutions and you report it to me in an e-mail before anybody else reports it to me (and before I find it myself), you will earn 1 point. I will reply to your e-mail with an e-mail telling you whether or not you earned a point. The points you earn this way will be added to your course score at the end of the semester, and I will send you an e-mail telling you the total number of points that you earned.


WeekDatesClass topics
1Mon Jan 12One.I.1 Solving Linear Systems: Gauss's Method
Wed Jan 14One.I.1 Solving Linear Systems: Gauss's Method (Group Work)
Fri Jan 16One.I.2 Solving Linear Systems: Describing the Solution Set
(H1 Due)
2Mon Jan 19Holiday: No Class
Wed Jan 21One.I.3 Solving Linear Systems: General = Particular + Homogeneous
Fri Jan 23One.I.3 Singular & Non-Singular Matrices; The Set Generated by a Set of Vectors
3Mon Jan 26One.III.1 Reduced Echelon Form: Gauss-Jordan Reduction (Group Work)
Wed Jan 28One.III.2 Reduced Echelon Form: The Linear Combination Lemma
(H2 Due)
Fri Jan 30In-Class Exam 1 Covering Chapter 1
4Mon Feb 2Two.I.1: Definition of Vector Space
Wed Feb 4Two.I.1: Definition of Vector Space
Fri Feb 6Two.I.2: Subspaces
5Mon Feb 9Two.I.2: Spanning Sets
(H3 Due)
Wed Feb 11Two.II.1: Linear Independence
Fri Feb 13Two.III.1: Basis
6Mon Feb 16Two.III.1: Basis (Lecture Notes)
(H4 Due)
Wed Feb 18Two.III.2: Dimension (Lecture Notes)
Fri Feb 20Two.III.3: Vector Spaces and Linear Systems (Lecture Notes)
7Mon Feb 23In-Class Exam 2 Covering Chapter 2
Wed Feb 25Three.I.1: Isomorphisms: Definitions and Examples (Lecture Notes)
Fri Feb 27Three.I.1: Isomorphisms: Definitions and Examples (Lecture Notes)
8Mon Mar 2Spring Break
Wed Mar 4
Fri Mar 6
9Mon Mar 9Three.I.2: Isomorphisms: Dimension Characterizes Isomorphism (Lecture Notes) (H5 Due)
Wed Mar 11TThree.II.1.Homomorphisms: Definition (Lecture Notes)
Fri Mar 13Three.II Homomorphisms (Lecture Notes) (H6 Due)
10Mon Mar 16Three.II.2.Homomorphisms: Range Space (Lecture Notes)
Wed Mar 18Three.II.2.Homomorphisms: Null Space (Lecture Notes)
(H7 Due)
Fri Mar 20Chapter 3 Sections I, II Leftovers and Review (Lecture Notes)
11Mon Mar 23In-Class Exam 3 Covering Chapter 3 Sections I, II
Wed Mar 25Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices (Lecture Notes)
Fri Mar 27Three.III.1: Computing Linear Maps: Representing Linear Maps with Matrices (Lecture Notes)
12Mon Mar 30Three.III.2: Computing Linear Maps: Any Matrix Represents a Linear Map (Lecture Notes)
Wed Apr 1Three.IV.1: Matrix Operations: Sums and Scalar Products; The Trace (Lecture Notes)
(H8 Due)
Fri Apr 3Three.IV.1: Matrix Operations: The Transpose (Lecture Notes)
13Mon Apr 6Three.IV.2: Matrix Operations: Matrix Multiplication (Lecture Notes)
Wed Apr 8Three.IV.2: Matrix Operations: Matrix Multiplication (Lecture Notes)
Fri Apr 10Three.IV.3 The Mechanics of Matrix Multiplication (Lecture Notes)
(H9 Due)
14Mon Apr 13Three.IV.4: Inverses (Lecture Notes)
Wed Apr 15In-Class Exam 4
Fri Apr 17Three.IV.4: Gauss's Method for computing Matrix Inverses (Lecture Notes)
15Mon Apr 20Five.II.1,2: Similarity, Diagonalizability (Lecture Notes)
Wed Apr 22Five.II.2,3 Diagonalizability, Eigenvalues and Eigenvectors (Lecture Notes)
Fri Apr 24Five.II.3 Eigenvalues and Eigenvectors (Lecture Notes)
(H10 Due)
16Mon Apr 27Comprehensive Final Exam 10:10am - 12:10pm in Morton 215 (Exam Information)

(page maintained by Mark Barsamian, last updated Aug 17, 2015)