MATH 230 Introduction to Linear Algebra*

This course includes the application of matrices, determinants, linear transformations and vector spaces.

Credits

3 Credits

Semester Contact Hours Lecture

45

Prerequisite

MATH 160 or MATH 170

MATH 230Introduction to Linear Algebra*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

I. General Information

Department

Mathematics & Engineering

II. Course Specification

Course Type

Program Requirement

Credit Hours Narrative

3 Credits

Semester Contact Hours Lecture

45

Prerequisite Narrative

MATH 160 or MATH 170

Grading Method

Letter grade

Repeatable

N

III. Catalog Course Description

This course includes the application of matrices, determinants, linear transformations and vector spaces.

IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

• Represent systems of linear equations using matrices, and use matrix properties and operations to solve those systems.
• Find the determinant of a matrix, and understand its properties and applications.
• Understand the basics of vector space theory (subspaces, linear independence, bases, • orthogonality, etc.) and use definitions and theorems to make conclusions about vectors and vector spaces.
• Use linear transformations to map from one vector space to another, and work with the matrix form of these transformations.
• Find the eigenvalues and eigenvectors of a matrix, and apply these concepts to real-world problems.

V. Topical Outline (Course Content)

Systems of Linear Equations Gaussian Elimination Matrices and Matrix Operations The Matrix Equation Ax=b Solution Sets of Linear Systems Linear Independence Linear Transformations Vector Equations The Inverse of a Matrix Characterizations of Invertible Matrices Partitioned Matrices Determinants and their Properties Cramer’s Rule and Volume Vector Spaces and Subspaces Null Spaces and Column Spaces Linearly Independent Sets; Bases Coordinate Systems The Dimension of a Vector Space Rank Change of Basis Eigenvectors and Eigenvalues The Characteristic Equation Diagonalization Eigenvectors and Linear Transformations Complex Eigenvalues Inner Product, Length and Orthogonality Orthogonal Sets Orthogonal Projections

VI. Delivery Methodologies