Introductory Linear Algebra

Offered By: Georgia Institute of Technology via edX

Course Description

Overview

The first of the two courses will introduce systems of equations, which 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. You will apply an algorithm for solving linear systems that will be used for computations and for gaining insight into the properties of linear systems. This insight will all you to reduce problems involving linear combinations of vectors to approaches that involve systems of linear equations. You will also explore linear independence and linear transformations. They have an essential role throughout applications of linear algebra in many areas of industry, science, and engineering.

In the second of these two courses you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept. You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.

Syllabus

Courses under this program:
Course 1: Linear Algebra I: Linear Equations

This course 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.

Course 2: Linear Algebra II: Matrix Algebra

This course takes you through roughly three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

Courses

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3 weeks, 5-6 hours a week, 5-6 hours a week
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Your ability to apply the concepts that we introduced in our previous course is enhanced when you can perform algebraic operations with matrices. At the start of this class, you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept.

You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.

Students taking this class are encouraged to first complete the first course in this series, linear equations.
0 reviews
3 weeks, 5-6 hours a week, 5-6 hours a week
View details

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. __

Taught by

Greg Mayer