Introduction to Linear Algebra

Revised: November 2006

Course Description

Systems of equations, matrices, vector spaces, and linear transformations. Prerequisites: Math 153, and Math 250. Three semester hours.

Objectives

   1. To provide clear understanding of the use of matrices in solving systems of linear equations;

   2. by use of examples and theory, to provide a thorough understanding of the concepts of vector spaces and subspaces;

   3. to acquaint students with linear transformations and eigenvalues.

Text

Gareth Williams, Linear Algebra with Applications, 5th Edition. Jones and Bartlett (publishers) 2005.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

• Chapter 1: Systems of Linear Equations (3 days)
        Sections 1 and 2, with selected applications in section 3 as time allows Systems of linear equations, Gauss-Jordan elimination, and selected applications (time allowing)
        Note: Inclusion of Gaussian elimination (Section 9.1) is also appropriate at this time.
• Chapter 2: Matrices (8 days)
        Sections 1-4, with selected applications from sections 5-7 as time allows Matrix operations, properties of matrix operations, symmetric matrices, matrix inverses, and applications (as time allows)
• Chapter 3: Determinants (5 days)
        Sections 1-4 Introduction to determinants, properties of determinants, evaluating determinants, and determinants with systems of equations
• Chapter 4: The Vector Space Rn (5 days)
        Sections 1-3; section 4 is optional Introduction to vectors and vector operations in Rn, dot product, norm, angle, and distance. Also, an introduction to linear transformations
        Note: Coverage of Section 4.3 (and 4.4, if covered) might be delayed, and introduced with Chapter 7.
• Chapter 5: General Vector Spaces (10 days)
        Sections 1-7 General vector spaces, subspaces, linear dependence and independence, bases and dimension, rank of a matrix, orthonormal vectors, and vector projections.
• Chapter 6: Eigenvalues and Eigenvectors (3 days)
        Section 1, with optional coverage of other sections (section 3 recommended if time allows) Eigenvalues and eigenvectors. Diagonalization of matrices and/or other applications as time allows.
• Chapter 7: Linear Transformations (2 or more days)
        Section 1, and additional material as time allows Linear transformations, kernel, and range. Coverage of additional material in this chapter is encouraged, if time remains at the end of the semester.
        Note: Coverage of this chapter might be combined with sections 4.3 and 4.4

    * Note: At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.