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Teaching & Academics Math Linear Algebra

Matrix Algebra Explained

Master Matrix Algebra Using Step by Step Lessons and Prepare yourself for Linear Algebra! Over 400 Practice Questions
Rating: 4.9 out of 54.9 (15 ratings)
74 students
Created by John Greene, M.A.
Last updated 7/2020
English
English [Auto]
30-Day Money-Back Guarantee

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

7 sections • 42 lectures • 8h 40m total length

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

  • Solving Systems of Linear Equations in Two Variables - Review
    36:23
  • Solving Systems of Linear Equations in Two Variables - Review Practice Test
    00:12
  • Solving Systems of Linear Equations in Two Variables - Review
    5 questions
  • Solving Systems of Linear Equations in Three Variables - Review
    33:32
  • Solving Systems of Linear Equations in Three Variables - Review Practice Test
    00:12
  • Solving Systems of Linear Equations in Three Variables - Review
    5 questions

  • Gaussian Elimination and Gauss-Jordan Elimination 2 x 2 System
    35:18
  • Gaussian Elimination and Gauss-Jordan Elimination 2 x 2 System Practice Test
    00:13
  • Gaussian Elimination and Gauss-Jordan Elimination 2 x 2 System
    5 questions
  • Gaussian Elimination and Gauss-Jordan Elimination 3 x 3 System
    39:26
  • Gaussian Elimination and Gauss-Jordan Elimination 3 x 3 System Practice Test
    00:13
  • Gaussian Elimination and Gauss-Jordan Elimination 3 x 3 System
    5 questions
  • Gaussian Elimination and Gauss-Jordan Elimination 4 x 4 System
    17:28
  • Gaussian Elimination and Gauss-Jordan Elimination 4 x 4 System Practice Test
    00:13
  • Gaussian Elimination and Gauss-Jordan Elimination 4 x 4 System
    5 questions

  • Finding the Determinant of an n x n Matrix
    29:38
  • Finding the Determinant of an n x n Matrix Practice Test
    00:12
  • Finding the Determinant of an n x n Matrix
    5 questions
  • Finding the Determinant of a Triangular Matrix
    15:22
  • Finding the Determinant of a Triangular Matrix Practice Test
    00:11
  • Finding the Determinant of a Triangular Matrix
    5 questions
  • Applications of Determinants - Area of a Triangle
    12:06
  • Applications of Determinants - Area of a Triangle Practice Test
    00:11
  • Applications of Determinants - Area of a Triangle
    5 questions
  • Applications of Determinants - Testing for Collinearity
    07:26
  • Applications of Determinants - Testing for Collinearity Practice Test
    00:11
  • Applications of Determinants - Testing for Collinearity
    5 questions
  • Applications of Determinants - Equations of a Line
    15:59
  • Applications of Determinants - Equations of a Line Practice Test
    00:11
  • Applications of Determinants - Equations of a Line
    5 questions

  • How to Find the Inverse of a Matrix
    48:25
  • How to Find the Inverse of a Matrix Practice Test
    00:12
  • How to Find the Inverse of a Matrix
    5 questions
  • Solving Matrix Equations Using the Inverse of a Matrix
    37:46
  • Solving Matrix Equations Using the Inverse of a Matrix Practice Test
    00:12
  • Solving Matrix Equations Using the Inverse of a Matrix
    5 questions
  • How to Find the Transpose of a Matrix
    04:08
  • How to Find the Transpose of a Matrix Practice Test
    00:12
  • How to Find the Transpose of a Matrix
    5 questions
  • How to Find the Adjoint (Adjugate) of a Matrix
    23:08
  • How to Find the Adjoint (Adjugate) of a Matrix Practice Test
    00:12
  • How to Find the Adjoint (Adjugate) of a Matrix
    5 questions
  • Inverse of a Matrix | Adjoint Method
    28:14
  • Inverse of a Matrix | Adjoint Method Practice Test
    00:11
  • Inverse of a Matrix | Adjoint Method
    5 questions

  • Cramer's Rule 2 x 2 System
    26:07
  • Cramer's Rule 2 x 2 System Practice Test
    00:12
  • Cramer's Rule 2 x 2 System
    5 questions
  • Cramer's Rule 3 x 3 System
    25:25
  • Cramer's Rule 3 x 3 System Practice Test
    00:12
  • Cramer's Rule 3 x 3 System
    5 questions

  • Matrix Algebra Final Exam
    27 questions

Instructor

John Greene, M.A.
Math Tutor
John Greene, M.A.
  • 4.7 Instructor Rating
  • 407 Reviews
  • 3,440 Students
  • 7 Courses

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.

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