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)
Corequisites
None
V. Other Pertinent Information
None
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
  1. Learning Goals:

    Course Specific:
    The student will be able to:
    1. solve a system of linear equations.
    2. reduce a matrix to reduced echelon form.
    3. solve a matrix equation.
    4. recognize a vector space, subspace.
    5. determine a basis for a vector space and the dimension of a vector space.
    6. determine coordinates for a vector relative to a given basis.
    7. perform dot product and apply to defining norm and orthogonality.
    8. recognize a linear mapping.
    9. determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces.
    10. find a matrix for a linear mapping.
    11. perform matrix products (composition of mappings),
    12. find an inverse of a nonsingular matrix (inverse of a mapping).
    13. apply matrix algebra to Leontief model, population model.
    14. evaluate determinant and relate to theory.
    15. recognize similar matrices.
    16. determine eigenvalues and eigenvectors.
    17. determine diganonability.
    18. apply theory of eigenvalues to Markov model.
  2. Planned Sequence of Topics and/or Learning Activities:

    1. Systems of Equations (8 lessons)


      1. Solutions using matrices
        Row reduction
        Existence and uniqueness of solutions
        Set of solutions as an example of a vector space
        Matrices
        Matrix equations

    2. Vector Spaces (12 lessons)


      1. Definitions
        Examples: Rn, C[0,1]
        Subspaces
        Independence and spanning
        Bases and coordinates

    3. Geometric Examples (2 lessons)


      1. R2 and R3
        Dot product
        Norm
        Orthogonality

    4. Linear Mappings (20 lessons)


      1. Homomorphisms, isomorphisms
        Null space of mapping
        Linear mappings
        Composition of mappings
        Product of matrices
        Inverse of a mapping
        Inverse of a matrix
        Algebra of matrices
        Determinants
        Leontief models
        Similar matrices
        Eigen vectors and values
        Diagonability
        Invariant subspaces
        Markov chains
        Quadratic forms - optional
  3. 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.

  4. 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