MAT 331: First Course in Linear Algebra

MAT 331
First Course in Linear Algebra
(3 credits)
Class Size: 10-25

Please contact Tavish Van Skoik (tvanskoi@syr.edu) if interested in this course.

Faculty: Hamidreza Rahmati, Assistant Teaching Professor, Syracuse University
Administrative Contact: Tavish Van Skoik, Assistant Director, Project Advance  

Course Catalog Description

Linear equations, n-dimensional euclidean space, linear independence, bases, linear transformations, matrices and determinants, eigenvalues and eigenvectors. Geometric aspects.

Course Overview

MAT 331 develops both the computational techniques of linear algebra and an understanding of why those techniques work, preparing students for advanced theory and for applications in engineering, computer science, economics, physics and computer graphics.

Orthogonality and Least Squares
a. Inner product, length and orthogonality
b. Orthogonal sets
c. Orthogonal projections
d. The Gram-Schmidt process

Linear Equations in Linear Algebra
a. Systems of linear equations and row reduction
b. Vector and matrix equations
c. Spans and solution sets
d. Linear independence
e. Linear transformations and their matrices

Matrix Algebra
a. Matrix operations and inverses
b. The Invertible Matrix Theorem
c. Applications to computer graphics
d. Subspaces of Rⁿ, column and null spaces
e. Basis, dimension and rank
f. Coordinates

Determinants
a. Properties of determinants
b. Cramer’s rule
c. Connections to area and volume

Eigenvalues and Eigenvectors
a. Eigenvalues and the characteristic equation
b. Diagonalization
c. Eigenvectors and linear transformations; complex eigenvalues (as time permits)

Pre- / Co-requisites

Completion of MAT 296 Calculus II.

Course Objectives

After completing this course, students will be able to:

  • Solve and analyze systems of linear equations.
  • Use the properties of vectors and matrices.
  • Determine the linear independence of a set of vectors.
  • Translate geometric notions into matrix and vector problems.
  • Represent linear transformations by matrices.
  • Use the concepts of vector subspaces, bases and linear independence to investigate properties of matrices.
  • Find eigenvalues and eigenvectors of a matrix and determine its diagonalizability.
  • Construct an orthogonal basis for a subspace.

Laboratory

N/A

Required Materials

Lay, Lay and McDonald’s Linear Algebra and Its Applications, sixth edition (Pearson)

ISBN-13: 9780136880929 (2020 update)

Instructor Recommendations

N/A