MTH 264 Introduction to Matrix Algebra

Lecture Hours: 2
Credits: 2

Introduction to matrix algebra; systematic solution to systems of linear equations; linear transformations; eigenvalue problems.

Prerequisite: Placement into WR 115 or completion of WR 090 and MTH 252Z with a grade of C or better; or consent of instructor.
Student Learning Outcomes:

Use Gaussian elimination to determine the solution set of a system of linear equations.
Determine whether a square matrix is invertible and find the inverse when it exists.
Calculate the determinant of a square matrix.
Determine if a set of vectors in Euclidean n-space is linearly independent or dependent.
Find the matrix representation of linear transformations with respect to standard bases.
Find the characteristic polynomial of square matrices.
Find the eigenvalues and eigenvectors of 2x2 and 3x3 matrices with real entries.

Content Outline

Vectors in Euclidean Space
- Vector Fundamentals
- Dot products
- Complex Numbers as Vectors
Matrices
- Matrix Operations
- Matrices as Linear Transformations
- Determinants of Square Matrices
- Inverse Matrices
Systems of Linear Equations
- Homogeneous and Nonhomogeneous Systems
- Matrix Representations of Systems
- Solutions Using Gaussian Elimination
- Solutions Using Matrix Inversion
Vector Spaces
- Linear Dependence and Independence
- Span
- Basis
Eigenvalues and Eigenvectors
- Characteristic Polynomials
- Finding Eigenvalues
- Finding Eigenvectors