Vector spaces, linear transformations, matrices and determinants, with applications to systems of linear equations, geometry and other selected topics. Prerequisite: Grade of C or higher in MATH 201.

Prerequisite(s) / Corequisite(s):

Grade of C or higher in MATH 201.

Course Rotation for Day Program:

Offered odd Fall.

Text(s):

Most current editions of the following:

Elementary Linear Algebra with Applications

By Anton & Rorres (Wiley) Recommended

Linear Algebra, A Modern Introduction

By Poole (Brooks-Cole) Recommended

Course Learning Outcomes

Demonstrate an understanding of concepts related to matrix solution of systems of linear equations.

Perform operations on vectors such as dot and cross products and interpret them geometrically.

Perform operations on matrices and classify them.

Demonstrate an understanding of basic concepts of linear transformation including eigenvalues, eigenvectors, kernel, rank, and nullity.

Demonstrate an understanding of basic concepts related to of vector spaces and bases.

Apply methods of linear algebra to solve problems in other branches of mathematics and in other disciplines.

Major Topics/Skills to be Covered:

Use matrices to solve systems of linear equations and interpret cases where solutions fail to exist.

Compute determinants and use them to solve systems of linear equations.

Compute the room, dot product and cross products of vectors and interpret these quantities geometrically.

Classify transformations as linear or nonlinear.

Verify the properties of a real vector space for specific examples.

Determine if a set of vectors is linearly independent or dependent.

Construct a basis for and compute the dimension of a vector space.

Analyze the relationship between row space, column space and null space of a coefficient matrix and its transpose with respect to solutions of a linear system of equations.

Use the Euclidean inner product to compute lengths, distances and angles.

Determine if bases are orthonormal or orthogonal.

Use properties of orthogonal matrices to change bases.

Compute eigenvalues and eigenvectors of linear transformations.

Use the theory of eigenvalues to diagonalize matrices.

Compute the kernel, rank and nullity of a linear transformation.

Determine if matrices are similar to each other.

Recommended maximum class size for this course: 30

NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section.
However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.