# Linear Equations

Massive Open Online Course
• Overview
• Course Content
• Requirements & Materials
Overview

## Linear Equations

Course Description

Systems of equations live at the heart of linear algebra. In this course you will explore fundamental concepts by exploring definitions and theorems that give a basis for this subject. At the start of this course we introduce systems of linear equations and a systematic method for solving them. 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 course you 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 in applications of linear algebra to many areas of industry, science, and engineering.

Course Content

SYSTEMS OF LINEAR EQUATIONS

ROW REDUCTION AND ECHELON FORMS

VECTOR EQUATIONS

THE MATRIX EQUATION

SOLUTION SETS OF LINEAR SYSTEMS

LINEAR INDEPENDENCE

AN INTRODUCTION TO LINEAR TRANSFORMS

LINEAR TRANSFORMS

Requirements & Materials
Prerequisites

Recommended

• High school algebra, geometry, and pre-calculus
Materials

Required

• Internet connection (DSL, LAN, or cable connection desirable)

### Who Should Attend

This course is designed for undergraduate students, advanced high school students, who are interested in pursuing any career path or degree program that involves linear algebra, or industry employees who are seeking a better understanding of linear algebra for their career development. ### What You Will Learn

• How to apply elementary row operations to solve linear systems of equations
• Parametric vector forms construction
• How to characterize and analyze linear systems and their solutions
• The concepts of span, linear independence, and pivots
• How to identify, analyze, and construct linear transformations
• Dependence relations between linearly dependent vectors
• The concept of linear independence ### How You Will Benefit

• Characterize linear systems in terms of their solution sets, consistency, and uniqueness.
• Characterize set of vectors in terms of linear combinations, their span, and how they are related to each other geometrically
• Apply linear algebra concepts to model, solve, and analyze real-world situations.
• Construct, or give examples of, mathematical expressions that involve vectors, matrices, and linear systems of linear equations.
• Analyze mathematical statements and expressions involving linear systems and matrices. For example, to describe solutions of systems in terms of existence and uniqueness.
• ##### Taught by Experts in the Field
•  - Abe Kani
President