Spring 2004
Mathematics 307 Section A1

Theory of Matrices

 Class Hours: MWF 10a.m.-10:50a.m. Instructor: Dr. Ling Long Office: 452 Carver Hall Phone: 515-294-8150 (O) E-mail: Office Hours: M 3:10pm-4pm, WF 11am –11:50am  (and by appointment)

Text Book:  Otto Bretscher, Linear Algebra with Applications, 2nd Ed (We will cover Chapters 1-7.)

Objectives:  Upon completion of this course you will be able to:

• Set up and solve systems of linear equations by Gauss-Jordan elimination.Use the reduced row echelon form to find the number of solutions of a linear system. Apply the definition of the rank of a matrix.
• Represent linear transformations by matrices, and calculate products and inverses of matrices.
• Apply the concepts of linear independence, basis and dimension. Find a basis of the kernel and the image of a linear transformation.
• Perform the Gram-Schmidt process. Find the matrix of an orthogonal projection. Find the least squares solution of a linear system by using the normal equations.
• Compute determinants by elimination or by Laplace expansion. Interpret the determinant as an area or volume. Use Cramer's rule.
• Use the characteristic polynomial to find eigenvalues of a matrix, with their algebraic multiplicities. For a given eigenvalue, find a basis of the associated eigenspace.
• Find the matrix of a linear transformation with respect to any basis. Use the idea of similarity of matrices. Find orthonormal eigenbases for symmetric matrices. Apply the spectral theorem.

Tentative Course Schedule:

# Topics

Time period (in week)

Chapter 1

Linear Equations

2

Chapter 2

Linear Transformations

2

Chapter 3

Subspaces of Rn and their Dimensions

2

First midterm exam: Feb 20

Chapter 4

Linear Spaces

1.5

Chapter 5

Orthogonality and Least Squares

2.5

Chapter 6 Determinants 1.5
Second midterm exam: April 2
Chapter 7 Eigenvalues and Eigenvectors 2.5

 Midterm Exams: There will be two in class midterm exams. The dates for midterms are Feb. 13, Friday and March 26 Friday. Final: The final will be 120 minutes long. The exact time and location will be posted on this website later. Homework: Homework assignments  will be collected regularly. Quizzes: There will be about 10 20-minute quizzes.   No make-up quiz will be given. Only the highest 8 quiz scores will be counted for the quiz grade in the end.  The quizzes mainly consist problems chosen from homework assignments.  No calculator will be allowed for quizzes.

 Grading Quizzes (20%) Midterm Exams (50%) Final Exam (30%)

Students are encouraged to study and work together but copying each other's work is not acceptable. Any cheating or dishonesty will be treated seriously, especially in an examination, and a grade of zero will usually be given. Final course grade will solely base on the performance on exams, quizzes and homework.

If you have a disability and require accommodations, please contact the instructor early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the Disability Resources (DR) office, located on the main floor of the Student Services Building, Room 1076, 515-294-6624.