# MAT 331 Linear Algebra

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### Course Description

The course covers Chapters 1-7 from the textbook: linear equations, vector spaces, matrices, linear transformations, determinants, eigenvalues, eigenvectors, etc.

MAT 331 meets for three hours of lecture per week.

### Prerequisites

Students must have earned at least a "C" in a course equivalent to MAT 271-Foundations of Higher Mathematics before enrolling in this course.

### Objectives

After completing MAT 331 the student should be able to
• solve systems of linear equations
• find the inverse of an invertible matrix
• evaluate determinants
• work with vectors
• identify bases of vector spaces
• find eigenvalues and eigenvectors of linear transformations

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 331.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics that are covered in MAT 331.

### Text

Larson and Edwards, Elementary Linear Algebra, 4th edition, Houghton Mifflin, 2000.

### List of Topics

• Systems of linear equations
• Introduction to Systems of Linear Equations
• Gaussian & Gauss-Jordan Elimination
• Matrices
• Operations with Matrices
• Properties of Matrix Operations
• The Inverse of a Matrix
• Elementary Matrices
• Determinants
• The Determinant of a Matrix
• Evaluation of a Determinant Using Elementary Operations
• Properties of Determinants
• Applications of Determinants
• Vector Spaces
• Vectors in Rn
• Vector Space
• Subspaces of Vector Spaces
• Spanning Sets and Linear Independence
• Basis and Dimension
• Rank of a Matrix and Systems of Linear Equations
• Coordinates and Change of Basis
• Inner Product Spaces
• Length and Dot Product in Rn
• Inner Product Spaces
• Orthonormal Bases: Gram-Schmidt Process
• Applications of Inner Product Spaces
• Linear Transformations
• Introduction to Linear Transformations
• The Kernel and Range of a Linear Transformation
• Matrices for Linear Transformations
• Eigenvalues and Eigenvectors
• Eigenvalues and Eigenvectors
• Diagonalization
• Symmetric Matrices and Orthogonal Diagonalization

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 331. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.