# Matrix Algebra Explained

## What you'll learn

- How to Solve Linear Systems Using Gaussian Elimination
- How to Solve Linear Systems Using Gauss-Jordan Elimination
- How to Place an Augmented Matrix in Row Echelon Form
- How to Place an Augmented Matrix in Reduced Row Echelon Form
- How to Add Matrices
- How to Subtract Matrices
- How to Multiply a Matrix by a Scalar
- How to Multiply Matrices
- How to Find the Inverse of a Matrix using Row Reduction
- How to Solve Linear Systems using Matrix Equations (Using the Inverse of a Matrix)
- How to Find the Determinant of a Matrix Using Laplace Expansion
- How to Find the Determinant of a 3 x 3 Matrix Using the Shortcut
- How to Find the Determinant of a Matrix in Upper Triangular Form 4 x 4 Shortcut
- How to Find the Transpose of a Matrix
- How to Find the Classical Adjoint (Adjugate of a Matrix)
- How to Find the Inverse of a Matrix Using the Determinant and the Adjoint (Adjugate)
- How to Solve a 2 x 2 Linear System Using Cramer's Rule
- How to Solve a 3 x 3 Linear System Using Cramer's Rule
- Applications of Determinants - Finding the Area of a Triangle
- Applications of Determinants - Testing for Collinearity
- Applications of Determinants - Finding the Equation of a Line Using Determinants

## Requirements

- Algebra 1
- Algebra 2 is helpful but not required

## Description

In this course, you will learn about the basics of matrices in algebra. While this is not a linear algebra course, it will serve to get you up to speed with most of the entry level topics taught in a linear algebra course. In this course, you will learn the following:

How to Solve Linear Systems Using Gaussian Elimination

How to Solve Linear Systems Using Gauss-Jordan Elimination

How to Place an Augmented Matrix in Row Echelon Form

How to Place an Augmented Matrix in Reduced Row Echelon Form

How to Add Matrices

How to Subtract Matrices

How to Multiply a Matrix by a Scalar

How to Multiply Matrices

How to Find the Inverse of a Matrix using Row Reduction

How to Solve Linear Systems using Matrix Equations (Using the Inverse of a Matrix)

How to Find the Determinant of a Matrix Using Laplace Expansion

How to Find the Determinant of a 3 x 3 Matrix Using the Shortcut

How to Find the Determinant of a Matrix in Upper Triangular Form 4 x 4 Shortcut

How to Find the Transpose of a Matrix

How to Find the Classical Adjoint (Adjugate of a Matrix)

How to Find the Inverse of a Matrix Using the Determinant and the Adjoint (Adjugate)

How to Solve a 2 x 2 Linear System Using Cramer's Rule

How to Solve a 3 x 3 Linear System Using Cramer's Rule

Applications of Determinants - Finding the Area of a Triangle

Applications of Determinants - Testing for Collinearity

Applications of Determinants - Finding the Equation of a Line Using Determinants

## Who this course is for:

- Students who want to learn the basics of Linear Algebra and be able to work with Matrices

## Course content

- Preview15:29
- 00:10Introduction to Matrices Practice Test
- 5 questionsIntroduction to Matrices
- 20:55Adding and Subtracting Matrices
- 00:11Adding and Subtracting Matrices Practice Test
- 5 questionsAdding and Subtracting Matrices
- 17:51Multiplying Matrices by a Scalar
- 00:11Multiplying Matrices by a Scalar Practice Test
- 5 questionsMultiplying Matrices by a Scalar
- 26:22Multiplying Matrices
- 00:10Multiplying Matrices Practice Test
- 5 questionsMultiplying Matrices

## Instructor

John Greene earned a bachelor's degree in Mathematics and a master's degree in Economics. Throughout his career, he has helped thousands of students ace their math and economics courses. John has a passion for learning, and wants to help students excel. John founded the site GreeneMath to help struggling students raise their grades in math, regardless of income.