Math 250 - Introduction to Linear Algebra. Sections 9 and 10. Fall 2007.

Contact Information
Instructor: Corey Hoelscher
Office: Hill Center, room 515.
Office Phone: 732-445-5935.
Office hours: Tuesdays 1:20-2:20 and 5:00-6:00
e-mail:

Announcements

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: 75
   1.2: 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, 29
   3.2: 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, 103
   6.2: 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