Date Adopted: July 1, 1998
Date Reviewed: December 1, 1999
Date Revised: 1999, 2007, 2012
Alabama
Department of
Postsecondary Education
Representing Alabama’s Public Two-Year College System
Jefferson State Community College
MTH 237
Linear Algebra
I.
MTH 237 Linear Algebra - 3 Semester Hours
Core Area III, AMTH Al 16 TMTH (Lec 3 hrs)
II.
Course Descriptio n
This course introduces the basic theory of linear equations and matrices, real
vector spaces, bases and dimension, linear transformations and matrices,
determinants, eigenvalues and eigenvectors, inner product spaces, and the
diagonalization of symmetric matrices. Additional topics may include quadratic
forms and the use of matrix methods to solve systems of linear differential
equations.
II.
Prerequisite
C or higher in MTH 126.
IV.
Textbook
Elementary Linear Algebra, 5th Edition, Stanley I. Grossman, Thomson
Brooks/Cole, 1994
V.
Course Objectives
The objective of this course is to provide an understanding of concepts, develop
competent skills, and demonstrate applications in the theory of elementary linear
algebra.
This course seeks to further the student's introduction to the more rigorous techniques and
thought processes of advanced mathematics.
VI..
Course Outline of Topics
A. This course shall include the following topics as a minimum:
1. Introduction to systems of linear equations
2. Gaussian elimination and Gauss-Jordan elimination
3. Applications of systems of linear equations
4. Operations with matrices
5. Properties of matrix operations
6. The inverse of a matrix
7. Elementary matrices
8. Applications of elementary matrices
9. Determinant of a matrix
10. Evaluation of a determinant using elementary operations
11. Properties of determinants
12. Applications of determinants
13. Vectors in n-space
14. Vector spaces
15. Subspaces
16. Spanning sets and linear independence
17. Basis and dimension
18. Rank of a matrix
19. Rank and systems of equations
20. Coordinates and change of basis
21. Applications of vector spaces
22. Length and dot product in n -space
23. Inner produ ct spaces
24. Orthonormal base: Gram-Schmidt process
25. Math models and least squares analysis
26. Applications of inner product spaces
27. Introduction to linear transformations
28. The kernel and range of a linear transformation
29. Matrices for linear transformations
30. Transition matrices and similarity
31. Applications of linear transformations
32. Eigenvalues and Eigenvectors
33. Diagonalization
34. Symmetric matrices and orthogonal diagonalization
35. Applications of eigenvalues and eigenvectors
B. Optional topics may include the following: 1. Quadratic forms
VII. Evaluation and Assessment
A. College requirements:
Examinations should be given by instructors periodically throughout their
courses. Faculty are encouraged to give evaluative work early in the term
so that students will have a clear understanding of the progress they are
making. Final examinations will be given in all classes, and all students
enrolled for academic credit will take the final examination. (College
Handbook, section 3.7)
B. Grading system as stated in the college catalog:
*A - Excellent (90-100)
*B - Good (80-89)
*C - Average (70-79)
D - Poor (60-69)
F - Failure (below 60)
W - Withdrawal (before last date to Withdraw)
WP - Withdrawal passing (after Last date to Withdraw )
WF - Withdrawal failure (after Last date to Withdraw)
I - Incomplete
AU - Audit
RW - Required
withdrawal
*Satisfactory grades
C. Criteria for evaluation:
1.
2.
3.
4.
Recitatio n
Daily assignments
Written a ssi gn ment s
To receive a grade of "C" or higher, the student must obtain an average
of at least 70% on written test(s) and other evaluation criteria as
determined by the instructor.
VIII. Class Activities
A.
B.
C.
D.
E.
Lecture
Recitation
Discussion
Individual Instruction
Testing
IX. General Course Competencies
A. The student will acquire knowledge of properties of determinants
and matrices.
B. The student will acquire knowledge of the properties of vector
spaces and subspaces.
C. The student will acquire knowledge of linear transformations.
D. The student will acquire knowledge of eigenvectors and eigenvalues.
X. Course Objectives Stated In Performance Terms
A. The student will demonstrate knowledge of the properties of
determinants and matrices by his/her ability to
1. use elementary row operations to solve systems of linear
equations.
2. use Gaussian elimination to solve systems of linear equations.
3. use the inverse of a matrix to solve systems of linear equations.
4. solve systems of homogeneous equations and state the conditions under
which a system will have solutions other than the trivial solution.
5. perform matrix addition, subtraction and multiplication.
6. state condition under which a matrix has an inverse and find the inverse of a
matrix.
7. evaluate a determinant of any order directly and by row
reduction.
8. evaluate a determinant by cofactor expansion.
9. use matrices and/or determinants to solve applied problems.
B. The student will demonstrate knowledge of vector spaces and subspaces by
his/her ability to
1. use the definition of a vector space to distinguish between
vector spaces and other spaces.
2. compute the inner product of two vectors in a vector space
and find the norm of a vector within a vector space.
3. define and find all the subspaces of a vector.
4. express any vector of a vector space as a linear combination of vectors
that span the space.
5. determine a set of basis vectors for a particular subspace.
6. determine whether or not a set of vectors forms a basis for a
particular space and find the dimension of the space.
7. verify that the axioms of an inner product space within a
particular space hold by calculation.
8. find the length, distance, and angle in an inner product space.
9. use the Gram-Schmidt process to transform the basis of an
inner product space to an orthonormal basis.
XI.
Attendance
Students are expected to attend all classes for which they are registered. Students who
are unable to attend class regularly, regardless of the reason or circumstance,
should withdraw from that class before poor attendance interferes with the student’s
ability to achieve the objectives required in the course. Withdrawal from class can
affect eligibility for federal financial aid.
XII.
Statement on Discrimination/Harassment
The College and the Alabama State Board of Education are committed to providing
both employment and educational environments free of harassment or discrimination
related to an individual’s race, color, gender, religion, national origin, age, or
disability. Such harassment is a violation of State Board of Education policy. Any
practice or behavior that constitutes harassment or discrimination will not be tolerated.
XIII. Americans with Disabilities
The Rehabilitation Act of 1973 (Section 504) and the Americans with Disabilities Act
of 1990 state that qualified students with disabilities who meet the essential functions
and academic requirements are entitled to reasonable accommodations. It is the
student’s responsibility to provide appropriate disability documentation to the
College. The ADA Accommodations office is located in FSC 300 (205-856-7731).