MATH260 Linear Algebra
Department of Science, Technology, Engineering & Mathematics: Mathematics
- I. Course Number and Title
- MATH260 Linear Algebra
- II. Number of Credits
- 3 credits
- III. Minimum Number of Instructional Minutes Per Semester
- 2250 minutes
- IV. Prerequisites
- MATH140 (C or better)
- V. Other Pertinent Information
- VI. Catalog Course Description
- Topics for this course include: vector spaces, linear transformations, matrix algebra, change of bases, similarity, diagonalization, eigenvalues and vectors; with application to solutions of systems of linear equations, linear programming, Leontief models, Markov chains, codes, and quadratic forms.
- VII. Required Course Content and Direction
Learning Goals:Course Specific:
The student will be able to:
- solve a system of linear equations.
- reduce a matrix to reduced echelon form.
- solve a matrix equation.
- recognize a vector space, subspace.
- determine a basis for a vector space and the dimension of a vector space.
- determine coordinates for a vector relative to a given basis.
- perform dot product and apply to defining norm and orthogonality.
- recognize a linear mapping.
- determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces.
- find a matrix for a linear mapping.
- perform matrix products (composition of mappings),
- find an inverse of a nonsingular matrix (inverse of a mapping).
- apply matrix algebra to Leontief model, population model.
- evaluate determinant and relate to theory.
- recognize similar matrices.
- determine eigenvalues and eigenvectors.
- determine diganonability.
- apply theory of eigenvalues to Markov model.
Planned Sequence of Topics and/or Learning Activities:
- Systems of Equations (8 lessons)
- Vector Spaces (12 lessons)
- Geometric Examples (2 lessons)
- Linear Mappings (20 lessons)
Solutions using matrices
Existence and uniqueness of solutions
Set of solutions as an example of a vector space
Examples: Rn, C[0,1]
Independence and spanning
Bases and coordinates
R2 and R3
Null space of mapping
Composition of mappings
Product of matrices
Inverse of a mapping
Inverse of a matrix
Algebra of matrices
Eigen vectors and values
Quadratic forms - optional
Assessment Methods for Core Learning Goals:All Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:Departmentally selected textbook. Details provided by the instructor of each course section. See Course Format.
- VIII. Teaching Methods Employed
- Use of lecture, class discussion, and WebCT.
Review/Approval Date - 4/06