Math 250 - Introduction to Linear Algebra. Sections 9 and 10. Fall 2007.
Contact Information
Instructor: Corey HoelscherOffice: Hill Center, room 515.
Office Phone: 732-445-5935.
Office hours: Tuesdays 1:20-2:20 and 5:00-6:00
e-mail:

Announcements
- In studying for the exam, I recommend the following, in order of importance: do the Final Exam Review below; redo the old exams and quizzes; look over the midterm reviews; and from the previous three, identify the areas you have the most difficulty with, reread those sections and do more problems on those topics.
- There will be a review session on Saturday (12/15) 2:00-4:00pm in Murray Hall, 213. Note room change!
- I will also have extra office hours on Sunday (12/15) 2:00-4:00pm in my office, Hill Center 515.
- There will be no office hours on Tuesday (12/18).
- You will be given the following list of equations and expressions on the final exam: Final Exam Equation Sheet. This is meant to focus your studying towards understanding and applying the concepts of the course instead of memorizing equations. However it by no means represents everything you will need to know for the exam. It is also your responsibility to know what each expression means and how to use it. As you study, you should make sure you can do all the problems on the exam reviews using only these equations and not your book or notes.
- Quiz, homework and exam grades are posted on Sakai.
General Information
Prerequisite: Calculus 2. Topics: Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. The main Math 240 website has more general information about this course.The text for the course is Spence, Insel, & Friedberg: "Elementary Linear Algebra: A Matrix Approach, 2nd Edition" along with the companion website with additional materials. Video lectures of a similar course are available from MIT's Linear Algebra webpage.
Homework
Doing homework problems is the best way to make sure you understand the material and to reinforce what you have learned. Every week there will be a homework assignment on the material covered in class. The assignments will be posted in the course calendar below and it is your responsibility to check this calendar for the assignments and due dates. The homeworks will be graded for completion and the quiz questions will generally be taken directly from the homework. Doing homework problems is the only way to really learn math. It is easy to sit through a lecture or read a book and think you understand everything. But when you sit down to solve problems you realize there are lots of holes in your knowledge. This is why the homework is an essential part of the course.
Quizzes
Quizzes are a good way for you to make sure you can solve important types of problems and they give you a bit more practice with the material. There will be a quiz each week in class that will cover the material from the previous homework. The quiz will usually consist of a few problems directly from the homework. The best way to study for the quizzes is to do the homework. If you know how to do all the problems on the homework then you will have no problem with the quiz. The two lowest quizzes will be dropped at the end of the semester and there will be no make-up quizzes for any reason.
Exams
There are two in-class midterm exams and one cumulative final exam. The midterms are tentatively scheduled for 10/10/07 and 11/14/07. Let me know now if you have any problems making these dates as make-up exams will only be given under extreme circumstances. The date for the final exam will be set by the university. No notecards or calculators will be allowed on any exam or quiz.
Grading
The grading will be roughly computed according to the following table.| Component | Weight |
| Quizzes | 15% |
| Homework | 5% |
| Midterm 1 | 23% |
| Midterm 2 | 23% |
| Final exam | 34% |
| Total | 100% |
Tentative syllabus
| Lecture | Sections | Topics | Notes |
|---|---|---|---|
| Wed 9/5 |
1.1, 1.2 | Matrices, Vectors, and Linear Combinations | |
| Mon 9/10 |
1.3 | Systems of Linear Equations | HW 1 due |
| Wed 9/12 |
1.4 | Gaussian Elimination | Quiz 1 |
| Mon 9/17 |
1.6 | Span of a Set of Vectors | HW 2 due |
| Wed 9/19 |
1.7 | Linear Dependence and Linear Independence | Quiz 2 |
| Mon 9/24 |
1.7, 2.1 | Homogeneous Systems, Matrix Multiplication | HW 3 due |
| Wed 9/26 |
2.1 | Matrix Algebra | Quiz 3 |
| Mon 10/1 |
2.3 App. E |
Invertibility and Elementary Matrices, Uniqueness of Reduced Row Echelon Form | HW 4 due |
| Wed 10/3 |
2.4, 2.5 | Inverse of a Matrix, Partitioned Matrices and Block Multiplication | Quiz 4 |
| Mon 10/8 |
2.7, 2.8 | Matrices as Linear Transformations, One-to-One and Onto Transformations | HW 5 due |
| Wed 10/10 |
Midterm exam 1 | Midterm 1 Review due | |
| Mon 10/15 |
3.1 | Determinants; Cofactor Expansions | |
| Wed 10/17 |
3.2 | Properties of Determinants | Quiz 5 |
| Mon 10/22 |
4.1 | Subspaces | HW 6 due |
| Wed 10/24 |
4.2 | Basis and Dimension | Quiz 6 |
| Mon 10/29 |
4.3 | Column Space and Null Space of a Matrix | HW 7 due |
| Wed 10/31 |
5.1 | Eigenvalues and Eigenvectors | Quiz 7 |
| Mon 11/5 |
5.2 | Characteristic Polynomial | HW 8 due |
| Wed 11/7 |
5.3 | Diagonalization of a Matrix | Quiz 8 |
| Mon 11/12 |
5.5 | Examples of Diagonalization | HW 9 due |
| Wed 11/14 |
Midterm exam #2 | Midterm 2 Review due | |
| Mon 11/19 |
6.1 | Geometry of Vectors; Projection onto a Line | |
| Wed 11/21 |
No class. Friday schedule. | Happy Thanksgiving | |
| Mon 11/26 |
6.2 | Orthogonal Sets of Vectors; Gram-Schmidt Process; QR factorization | Quiz 9 |
| Wed 11/28 |
6.3 | Orthogonal Projection; Orthogonal Complements | HW 10 due |
| Mon 12/3 |
6.4 | Least Squares; Normal Equations | Quiz 10 |
| Wed 12/5 |
6.5, 6.6 | Orthogonal Matrices; Diagonalization of Symmetric Matrices | HW 11 due |
| Mon 12/10 |
6.6 | Diagonalization of Quadratic Forms, Spectral Decomposition for Symmetric Matrices | Quiz 11 |
| Wed 12/12 |
Review for final | HW 12 due |
Homework assignments
Read the following description of how to present your work.
HW 1:
Reading:Sections 1.1 and 1.2
Problems:
1.1: 1, 3, 5, 9, 17, 19, 23, 25, TF: 37-56, 71, 75, 79, 81*, 82
HW 2:
Reading:Sections 1.2, 1.3 and 1.4
Presenting Your Work
Problems:
1.2: 1, 3, 9, 15, 17, 19, 29, 31, 35, 37, 39, TF: 45-63, 67, 68, 75, 76, 77, 78
1.3: 1, 3, 7, 9, 11, 23, 25, 39, 41, 43, 45, 47, 49, 51, 53, 55, TF: 57-76, 81
1.4: 1, 3, 5, 7, 11, 13, 17, 19, 23, 27, 35, 37, 43, TF: 53-72, 74-78, 81-84, 87-91
HW 3:
Reading:Sections 1.6 and 1.7
Problems:
1.6: 1, 3, 17, 19, 21, 23, 25, 27, 29, 31, 33, 39, 43, TF: 45-64, 70, 72
1.7: 1, 5, 13, 15, 23, 25, 29, 33
HW 4:
Reading:Sections 1.7 and 2.1
Problems:
1.7: 39, 41, 51, 53, 57, TF: 63-82, 87*, 89
2.1: 5, 7, 9, 11, 13, 15, 17, 19, 22, 23, 25, 27, 29, 31, TF: 33-50
HW 5:
Reading:Sections 2.3, 2.4 and 2.5
Problems:
2.3: 1, 3, 9, 11, 13, 17, 19, 23, 25, 29, 31, TF: 33-52, 54, 59, 61, 67, 69, 71, 83
2.4: 1, 3, 7, 9, 19, 27, 29, TF: 35-54, 64
2.5: 1, 3, 9, 35, 37, 39
Midterm 1 Review:
1.1: 751.2: 15, 66, 71, 78
1.3: 77
1.4: 3, 13, 15, 29, 75, 81
1.6: 17, 25, 33, 67
1.7: 17, 25, 47, 85
Chapter 1 Review: TF: 1-17, 35, 48, 51, 61, 67, 71
2.1: 25, 27, 63
2.3: 13, 17, 29, 63, 69
2.4: 13, 29, 57
Chapter 2 Review: 33, 45
HW 6:
Reading:Sections 2.7 (but not in detail), 2.8, 3.1 and 3.2
Problems:
2.7: 21, 27, 29
2.8: 1, 3, 13, 15, 21, 29, 35, 65
3.1: 1, 3, 9, 11, 13, 14, 15, 21, 23, 27, 29, 31, 37, 43, TF: 45-63
3.2: 5, 6, 7, 8, 11, 13, 17, 21, 27, 33, TF: 39-58, 59, 63, 67, 69-74
HW 7:
Reading:Sections 4.1 and 4.2
Problems:
4.1: 1, 3, 5, 9, 11, 13, 19, 21, 27, 29, 33, TF: 43-51, 57-62, 67, 69, 72, 73, 74, 78, 81, 83, 85, 89, 93
4.2: 1, 3, 5, 7, 17, 19, 21, 25, 27, TF: 33-50, 53, 54, 59, 63, 65
HW 8:
Reading:Sections 4.3 and 5.1
Problems:
4.3: 1, 3, 5, 7, 9, 11, 15, 17, 19, 25, 27, TF: 41-57, 59-60, 63, 65, 69, 73-75, 83
5.1: 1, 3, 7, 9, 13, 17, 23, TF: 41-46, 55-60, 61, 63, 64, 66, 67, 69, 72, 73, 74
HW 9:
Reading:Sections 5.2 and 5.3
Problems:
5.2: 1, 5, 9, 11, 13, 15, 17, 19, 21, 41, 47, TF: 53-72, 79, 81, 85, 86
5.3: 1, 3, 5, 7, 11, 15, 17, 19, TF: 29-48, 49, 51, 55, 57, 61, 63, 65, 73, 77, 78, 81, 82, 83, 85
Midterm 2 Review:
3.1: 17, 27, 293.2: 13, 29, 63,69, 73
Chapter 3 Review: 39
4.1: 11, 19, 72, 73, 74, 83, 89
4.2: 7, 19, 59
4.3: 3, 19, 74
Chapter 4 Review: 31, 49
5.1: 7, 63, 65, 67, 69
5.2: 5, 7, 17, 73, 82
5.3: 1, 9, 17, 49, 51, 57, 63, 73
HW 10:
Reading:Sections 6.1, 6.2 and the subsection of 5.5 on systems of differential equations
Problems:
5.5: 45, 55, 61
6.1: 3, 5, 7, 9, 11, 13, 15, 17, 25, 29, 33, 37, 43, 49, 51, 53, TF: 61-80, 95, 97, 98
6.2: 1, 3, 7, 9, 13, 17, 21, 25, 29, 33, 37, TF: 41-52, 55
HW 11:
Reading:Sections 6.3 and 6.4
Problems:
6.3: 1, 5, 9, 11, 17, 19, 21, TF: 33-56, 59, 61, 67, 69, 71, 73, 75
6.4: 1, 5, 17, 21, TF: 28-32
HW 12: (due Wed 12/12)
Reading:Sections 6.5 and 6.6
Problems:
6.5: 3, 7, 9, 11, TF: 17, 21-29, 49
6.6: 3, 5, 13, 15, 17, 19, TF: 21-40, 59*
Final Exam Review: (due at final)
6.1: 7, 13, 45, 49, 53, 87, 92, 1036.2: 5, 15, 19, 31, 39, 63
6.3: 7, 13, 29, 61, 68
6.4: 3, 17, 23
6.5: 13, 49
6.6: 1, 17
Chapter 6 Review: TF: 1-17, 45
You should also look over the midterm reviews and do some problems from those sections.
TF denotes true or false questions
* denotes especially challenging problems
Be sure to check all your answers in the back of the book.
Last modified: September 10, 2007