Student Effort:

30 hours

Description

The content in this module takes you through the first three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

This module begins with an introduction to systems of linear equations. Systems live at the heart of linear algebra and as such, are the primary subject of this course. The definitions and theorems that are introduced in this module will provide a basis for the remainder of this course.

At the start of this course we introduce a systematic method for solving linear systems of equations. This algorithm will be used for computations throughout the course as you investigate applications of linear algebra and more complex algorithms for analyzing them.

Later in this module we will later see how a system of linear equations can be represented in other ways, which can reduce problems involving linear combinations of vectors to approaches that involve systems of linear equations. Towards the end of the course we explore linear independence and linear transformations. They have an essential role throughout our course, and play an essential role in applications of linear algebra to many areas of industry, science, and engineering.

Learning Outcomes

At the completion of this module, students should be able to do the following.

Evaluate mathematical expressions to compute quantities that deal with linear systems.
Characterize a linear system in terms of the number of solutions, and whether the system is consistent or inconsistent.
Apply elementary row operations to solve linear systems of equations.
Characterize a set of vectors in terms of linear combinations, span, and how they are related to each other geometrically.
Characterize a set of vectors and linear systems using the concept of linear independence.
Construct dependence relations between linearly dependent vectors.
Identify and construct linear transformations of a matrix.
Characterize linear transformations as onto and/or one-to-one.