Linear Algebra I
1. Catalog Description
MATH 206 Linear Algebra I (4)
Matrices, inverses, linear systems , determinants, eigenvalues, eigenvectors,
vector spaces, linear
transformations, applications. 4 lectures. Prerequisite : MATH 143 or consent of
instructor.
2. Required Background or Experience
Math 143 or consent of instructor.
3. Learning Objectives
After successfully completing this course, the student should possess a working
knowledge
of the following:
a. The concept of matrices and their role in linear algebra and applied
mathematics.
b. A complete understanding of linear systems Ax = b, and the role of rank,
subspace,
linear independence , etc. in the analysis of these systems.
c. Eigenvalues and eigenvectors of matrices and their computation.
d. The concept of determinant and its properties.
e. The concepts of vector space and linear maps when the vector space is Rn.
f. The role of decomposition of matrices such as A = LU or A = QR in solving
linear
systems or least squares approximations .
g. Important definitions in linear algebra and the ability to do very elementary
proofs.
h. Re-emphasize the concept and precise definition of a function and give
specific
examples within the context of this particular course.
4. Text and References
Lay, David C., Linear Algebra and its Applications, 3rd ed., Addison -Wesley,
2003
Bretscher, Otto, Linear Algebra with Applications, 3rd ed., Prentice-Hall, 2004
5. Minimum Student Materials
Paper, pencils, and notebook. A calculator with the capability to do matrix
manipulation
is recommended for applications.
6. Minimum University Facilities
Classroom with ample chalkboard space for class use. Use of a computer lab is
optional.
7. Content and Method
The following outline is based on the Linear Algebra Curriculum Study Group
Recommendations
for a first course in linear algebra. For a detailed description of these
recommendations, see the
January 1993 issue of The College Mathematics Journal or the course supervisor.
The sections
listed are for Lay’s 3rd edition. It is easy to go too slowly in chapter one.
Overheads are available
for examples of systems of linear equations .
| Topics | Lessons | |
| Sections 1.1 – 1.9 | Systems of linear equations | 9 |
| Sections 2.1 – 2.4 | Matrix and vector operations , factorizations | 4-5 |
| Sections 2.8 – 2.9 | Properties of
Rn (linear combinations, bases, spanning set, dimensions, dimension equation) |
5-7 |
| Sections 3.1 – 3.3 | Determinants | 2-3 |
| Sections 5.1 – 5.3 | Eigenvalues and eigenvectors | 3-5 |
| Sections 6.1 – 6.3 | Orthogonality (orthogonal projections,
Gram-Schmidt orthogonalization, QR factorizations ) |
3-5 |
| Section 7.1 | Diagonalization of symmetric matrices | 1-2 |
|
Total |
27-36
|
Recommended Supplementary Topics
If time permits, more applications, such as 1.10, 2.6, 2.7, 4.9, 5.6. Do not
cover abstract vectors
spaces in depth; this will cause too much overlap with
Math 306.
Method
Lecture, classroom discussion, and computer projects at discretion of
instructor. Include
proofs at appropriate levels in lectures, homework, and/or
discussion .
8. Methods of Assessment
Assigned problem sets, scheduled examinations, and possibly computer projects.
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