#### Prerequisites & Bulletin Description

#### Course Objectives

Students will:

- Use matrix methods to solve systems of linear equations and analyze overdetermined and underdetermined systems
- Calculate matrix sums, products and inverses
- Use dot product, cross product and orthogonality to find equations for planes, distance between two lines, and perform other geometric calculations
- Find bases for subspaces (e.g. kernels) of real Euclidean space and prove simple theorems about subspaces
- Evaluate determinants of matrices and recognize special cases when the determinant of a matrix is zero.
- Find eigenvalues and eigenvectors including defective cases, recognize special eigenvalue properties of symmetric matrices, and prove simple theorems about eigenvalues and eigenvectors.
- Perform at least one of the operations above with software

#### Evaluation of Students

Student will demonstrate their mastery of the first six objectives on frequent graded homework assignments or quizzes, midterm and final examinations. Students will also complete at least one graded assignment requiring the use of software to perform matrix and vector calculations.

#### Course Outline

Topics |
Number of Weeks |

Linear equations | 3 |

Matrices and inverses | 2 |

Vector geometry of lines and planes | 2 |

Subspaces of real Euclidean space, bases and dimension | 3 |

Determinants | 2 |

Eigenvalues and eigenvectors | 3 |

#### Textbooks & Software

Howard Anton, *Elementary Linear Algebra*, 8th edition, Wiley, 2000

Otto Bretscher, *Linear Algebra with Applications*, Prentice Hall, 2001

Lawrence E. Spence, Arnold J. Insel, Stephen H. Friedberg, *Elementary Linear Algebra: A Matrix Approach*, Prentice Hall, 2000

Submitted by: David Meredith

Date: Dec 2nd, 2002