I. Course Course Course
Prefix Number Name Credit Lecture Lab
MAT 260
Linear Algebra 3 3 0
II. Prerequisite:
MAT 251 with a grade of C or better.
III. Course
Description:
Course covers matrices and the algebra of linear systems. Content includes equations, vector spaces, real inner product spaces, linear transformations, determinants, eigenvalues, eigenvectors, diagonability, quadratic forms and symmetric matrices. Calculators/computers used when appropriate.
IV. Course
Objectives:
A. Use basic matrix operations and the algebra of matrices in practical problems. Possible applications may be drawn from areas such as Kirchoff’s laws, Leontieff model of an interacting economy, Markov chains, method of least squares, singular value decomposition and Fourier coefficients of a function.
B. Understand the concepts of vector spaces, subspaces, basis, independence and dependence, dimension, coordinates, rank of a matrix, inner product.
C. Use the dependency relationship algorithm and the Gram-Schmidt orthogonizational process.
D. Understand linear transformations, range and null space of a linear transformation, the correspondence principle and similarity.
E. Understand properties of the determinant function and the cofactor expansion of determinants.
F. Understand the concepts of eigenvalues and eigenvectors.
G. Understand the concepts of quadratic forms.
V. Academic
Integrity:
Students and employees at
· cheating,
· plagiarism (turning in work not written by you, or lacking proper citation),
· falsification and fabrication (lying or distorting the truth),
· helping others to cheat,
· unauthorized changes on official documents,
· pretending to be someone else or having someone else pretend to be you,
· making or accepting bribes, special favors, or threats, and
· any other behavior that violates academic integrity.
There are serious consequences to violations of the academic integrity policy. Oakton’s policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.
Details of the Code of Academic
Conduct can be found in the Student Handbook.
VI. Outline
of Topics:
A. Systems
of Linear Equations and Matrices
1
Gaussian elimination
2
Homogeneous systems of linear
equations
3
Matrices and matrix arithmetic
4
Matrix invertibility
5 Applications
B. Vector
Spaces
1. Euclidean n-space
2. Linear independence
3. Basis and dimension
4. Rank of a matrix
5. Inner product spaces
6. Orthonormal
bases and projections
C. Linear
Transformations
1. Properties, range and null space
2. Matrix representations, products and
inverses
3. Similarity
D. Determinants
1. The determinant function and evaluation
2. Properties of determinants
3. Cofactor expansion
4. Applications including Cramer's Rule
1. Eigenvalues
and eigenvectors of linear transformations
2. Diagonalization
F. Quadratic
forms
1.
Symmetric
matrices
G. Recommended
Technology
1.
Use
of technology to perform matrix computations
2.
Use
of technology to determine matrix products and inverses
3. Use of technology to evaluate determinants
VII.
Methods of Instruction:
(To be completed by instructor)
Methods of presentation can include lectures, discussion,
experimentation, audio-visual aids, small-group work and regularly assigned
homework. Calculators/computers will be used when appropriate. Mathematica is available for use at the College at no
charge.
VIII. Course
Practices Required:
(To be completed by instructor)
VIII.
Instructional Materials:
Required Textbook: http://www.oakton.edu/acad/dept/mcs/mat/textbooks.htm
A computer
algebra system is required.
X. Methods
of Evaluating Student Progress:
(To be determined and announced by the instructor)
Evaluation methods can include
grading homework, chapter or major tests, quizzes, individual or group
projects, calculator/computer projects and a final examination.
XI. Other Course Information:
If you have a documented learning,
psychological, or physical disability you may be entitled to reasonable
academic accommodations or services. To
request accommodations or services, contact the ASSIST office in the
Effective beginning term: ___Fall 2004__________ Ending term: ___________
(term) (year) (term) (year)
Syllabus prepared by: J. Hasset & R. Sompolski Date:
Reviewed by Dept/program chair: R. Sompolski Date: ____________
Approved by Dean: J. Kotowski Date: ____________