MA211 INTRODUCTION TO MATRIX THEORY AND LINEAR ALGEBRA (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 161 or permission of instructor

General Introduction and Goals

MA 211 provides the opportunity to develop computational skills, to pursue mathematical abstraction, and to explore significant applications. It is the aim of this course to expose students to all three aspects but with primary emphasis given to the first two. About equal time will be given to computations and the mathematical abstractions that underlie the subject. Because this is the first course in which students see an abstract mathematical system and in which they are expected to do mathematical proofs, MA 211 is a prerequisite for most of the 300-level mathematics courses.

In this course, the student will:

• develop the skills required to represent and manipulate vectors in n-dimensional space;
• develop the basic skills of matrix algebra;
• develop the computational skills needed for the reduction of matrices to normal forms;
• understand the axiomatic treatment of vector spaces;
• develop an understanding of the notion of linear transformations and their representations;
• explore the applications of the general techniques of linear algebra;
• develop a writing style appropriate for mathematical exposition;
• develop the ability to construct careful proofs of theorems.

Course Content

1. Vector Notations
2. Matrix Algebra
   • Addition and multiplication
   • Applications of matrix multiplication
   • Elementary Matrices
   • Inverse Matrices
   • Triangular Matrices
3. Matrices and Geometry
   • Matrix representation of linear transformations
   • Geometric transformations and their matrix representations
4. Determinants
5. Vector Spaces
   • Basis and Dimension
   • Linear Transformations
   • Metric Concepts (inner products)
   • Eigenvectors and Eigenvalues and applications

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