# Linear Algebra

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

** Course Name: **
Linear Algebra

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

**II. Prerequisite **

MAT 251 with minimum grade of C.

**III. Course (Catalog) 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. Learning Objectives **

1. Use basic matrix operations and the algebra of matrices to solve practical problems. Applications include topics such as Kirchoff’s laws, the Leontieff model of an economy, Markov chains, least squares methods, singular value decomposition and Fourier coefficients of a function.

2. Determine if a set is a vector space or subspace.

3. Calculate bases, dimension and rank of a matrix, and use inner products to find lengths, projections, and angles between vectors.

4. Determine dependence and independence of a set of vectors.

5. Use the Gram-Schmidt process to find an orthogonal basis for a vector space.

6. Apply algebraic methods to construct, analyze and evaluate the following features of linear transformations: their matrices, whether they are one-to-one or onto, their range and null spaces, and their similarity.

7. Apply properties of the determinant function, expand determinants using cofactors, and calculate determinants.

8. Calculate eigenvalues and eigenvectors.

9. Classify quadratic forms and find a basis for which a quadratic form has no cross-terms.

2. Determine if a set is a vector space or subspace.

3. Calculate bases, dimension and rank of a matrix, and use inner products to find lengths, projections, and angles between vectors.

4. Determine dependence and independence of a set of vectors.

5. Use the Gram-Schmidt process to find an orthogonal basis for a vector space.

6. Apply algebraic methods to construct, analyze and evaluate the following features of linear transformations: their matrices, whether they are one-to-one or onto, their range and null spaces, and their similarity.

7. Apply properties of the determinant function, expand determinants using cofactors, and calculate determinants.

8. Calculate eigenvalues and eigenvectors.

9. Classify quadratic forms and find a basis for which a quadratic form has no cross-terms.

**V. Academic Integrity **

Students and employees at Oakton Community College are required to demonstrate academic integrity
and follow Oakton's Code of Academic Conduct. This code prohibits:

• 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.

• 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. Sequence 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

E. Eigenvalues and Eigenvectors

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

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

E. Eigenvalues and Eigenvectors

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.

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

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, media-based, hybrid or online course.

**VIII. Course Practices Required **

(To be completed by instructor)

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

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.

**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.

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 **

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

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.

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.