MATH260 Linear Algebra

Department of Science, Technology, Engineering & Mathematics: Mathematics

  1. Course Number and Title

    MATH260 Linear Algebra

  2. Number of Credits

    3 credits

  3. Minimum Number of Instructional Minutes Per Semester

    2250 minutes

  4. Prerequisites

    MATH140 (C or better)

    Corequisites

    None

  5. Other Pertinent Information

    None

  6. 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.

  7. 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)


          2. 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)


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

      3. Geometric Examples (2 lessons)


          4. R2 and R3
          Dot product
          Norm
          Orthogonality

      4. Linear Mappings (20 lessons)


          5. 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.

  8. Teaching Methods Employed

    Use of lecture, class discussion, and WebCT.

Review/Approval Date - 4/06