# Linear Algebra

**I. Course Prefix/Number: **
MAT 260

** Course Name: **
Linear Algebra

** Credits: **
3 (3 lecture; 0 lab)

**II. Prerequisite **

**III. Course (Catalog) Description **

**IV. Learning Objectives **

- Apply basic matrix methods to solve systems of linear equations. Determine whether the equations are linearly independent and how that affects the solution.
- Apply course content to applications which may include topics such as Kirchoff’s laws, Leontieff economic models, Markov chains, least squares methods, image processing, and statistics.
- Apply algebraic methods to construct, analyze, and evaluate the following features of linear transformations: matrices and factorizations, one-to-one, onto, range, column space, null space, and similarity.
- Calculate determinants, cofactor expansions, eigenvalues and eigenvectors. Use diagonalization to compute bases for an eigenspace.
- Apply the definitions of vector space and subspace to establish coordinate systems and a change of basis.
- Calculate bases, dimension and rank of a matrix, use inner products to find lengths, projections, angles between vectors and to determine linear dependence or independence of a set of vectors.
- Use the Gram-Schmidt process to find an orthogonal basis for a vector space.
- Use symmetric matrices and diagonalization to classify quadratic forms and find a basis for which a quadratic form has no cross-terms.

**V. Academic Integrity and Student Conduct **

• 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.

Please review the Code of Academic Conduct and the Code of Student Conduct, both located online at

www.oakton.edu/studentlife/student-handbook.pdf

**VI. Sequence of Topics **

- Systems of Linear Equations and Matrices
- Gaussian elimination
- Homogeneous systems of linear equations
- Matrices and matrix arithmetic
- Matrix invertibility
- Applications

- Vector Spaces
- Euclidean n-space
- Linear independence
- Basis and dimension
- Rank of a matrix
- Inner product spaces
- Orthonormal bases and projections

- Linear Transformations
- Properties, range and null space
- Matrix representations, products and inverses
- Similarity

- Determinants
- The determinant function and evaluation
- Properties of determinants
- Cofactor expansion
- Applications including Cramer's Rule

- Eigenvalues and Eigenvectors
- Eigenvalues and eigenvectors of linear transformations
- Diagonalization

- Quadratic forms
- Symmetric matrices

- Recommended Technology
- Use of technology to perform matrix computations
- Use of technology to determine matrix products and inverses
- Use of technology to evaluate determinants

**VII. Methods of Instruction **

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, Derive*, and TI-92 calculators are available for use at the College at no charge.

Course may be taught as face-to-face, hybrid or online course.

**VIII. Course Practices Required **

Course may be taught as face-to-face, media-based, hybrid or online course.

**IX. Instructional Materials **

**Note:**Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page http://www.oakton.edu/academics/academic_departments/math/syllabi

A computer algebra system is required.

**X. Methods of Evaluating Student Progress **

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 Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

Oakton Community College is committed to maintaining a campus environment emphasizing the dignity and worth of all members of the community, and complies with all federal and state Title IX requirements.

Resources and support for

- pregnancy-related and parenting accommodations; and
- victims of sexual misconduct

Resources and support for LGBTQ+ students can be found at www.oakton.edu/lgbtq.