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Matrix Algebra Explained

4.8 Filled star Filled star Filled star Filled star Half star
Based on 45 ratings
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John Greene, M.A.

In this course, you will master 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:

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In this course, you will master 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

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What's inside

Syllabus

In this lesson, we will learn how to add and subtract matrices.

Students will learn how perform operations with matrices.

In this lesson, we will learn about the basics of matrices.

Read more

Practice test for our lesson on introduction to matrices.

This quiz will test your knowledge of basic concepts regarding to matrices.

Practice test for adding and subtracting matrices.

This quiz will test your knowledge of how to add and subtract matrices.

In this lesson, we will learn how to multiply a matrix by a scalar, which is a real number that is not inside of a matrix.

Practice test for multiplying matrices by a scalar.

This quiz will test your knowledge of how to multiply a matrix by a scalar.

In this lesson, we will learn how to multiply two matrices together.

Practice test for multiplying matrices.

This quiz will test your knowledge of how to multiply matrices.

In this lesson, we will review how to solve a system of linear equations using substitution, elimination and graphing.

Practice Test for Solving Systems of Linear Equations in Two Variables.

This quiz will test your knowledge of how to solve a system of linear equations in two variables.

In this lesson, we will review how to solve a system of linear equations in three variables.

Practice Test for Solving Systems of Linear Equations in Three Variables.

This quiz will test your knowledge of how to solve a system of linear equations in three variables.

In this lesson, we will learn how to solve a linear system in two variables using gaussian elimination and gauss-jordan elimination.

Practice test for our lesson on Gaussian Elimination and Gauss-Jordan Elimination 2 x 2 System.

This quiz will test your knowledge of how to solve a 2 x 2 system using Gaussian elimination and Gauss-Jordan elimination.

In this lesson, we will continue to learn how to solve a linear system in two variables using gaussian elimination and gauss-jordan elimination. In this section, we will look at 3 x 3 systems.

Practice test for our lesson on Gaussian Elimination and Gauss-Jordan Elimination 3 x 3 System.

This quiz will test your knowledge of how to solve a 3 x 3 linear system using Gaussian Elimination and Gauss-Jordan Elimination.

In this lesson, we will continue to learn how to solve a linear system in two variables using gaussian elimination and gauss-jordan elimination. In this section, we will look at 4 x 4 systems.

Practice test for our lesson on Gaussian Elimination and Gauss-Jordan Elimination 4 x 4 System

This quiz will test our knowledge of how to solve a 4 x 4 linear system using Gaussian Elimination and Gauss-Jordan Elimination.

In this lesson, we will cover how to find the determinant of an n x n matrix using the laplace expansion method. We will also learn the shortcut for a 3 x 3 matrix.

Practice test for our lesson on finding the determinant of an n x n matrix.

This quiz will test your knowledge of how to find the determinant of an n x n matrix.

In this lesson, we will learn how to find the determinant of a matrix that is in triangular form. This will help us when we seek the determinant of a matrix that is a 4 x 4 or higher.

Practice test for finding the determinant of a triangular matrix.

This quiz will test your knowledge of how to find the determinant of a triangular matrix.

In this lesson, we will learn how to use determinants to find the area of a triangle.

Practice test for applications of determinants - area of a triangle.

This quiz will test your knowledge of how to find the area of a triangle using determinants.

In this lesson, we will learn how to determine if three points are collinear using matrices.

Practice test for applications of determinants - test for collinearity.

This quiz will test your knowledge of how to determine if three points are collinear using matrices.

In this lesson, we will learn how to determine how to use determinants to write the equation of a line.

Practice test for applications of determinants - equation of a line.

This quiz will test your knowledge of how to find the equation of a line using determinants.

In this lesson, students will learn how to find the inverse of a matrix.

Practice test for how to find the inverse of a matrix.

This quiz will test your knowledge of how to find the inverse of a matrix.

In this lesson, we will learn how to solve linear systems using matrix equations.

Practice test for solving matrix equations using the inverse of a matrix.

This quiz will test your knowledge of how to solve matrix equations using the inverse of a matrix.

In this lesson, students will learn how to find the transpose of a matrix.

Practice test for how to find the transpose of a matrix.

This quiz will test your knowledge of how to find the transpose of a matrix.

In this lesson, we will learn how to find the adjoint (adjugate) of a matrix.

Practice test for how to find the adjoint of a matrix.

This quiz will test your knowledge of how to find the adjoint (adjugate) of a matrix.

In this lesson, students will learn how to find the inverse of a matrix using the determinant and the adjoint.

Practice test for the inverse of a matrix.

This quiz will test your knowledge of how to find the inverse of a matrix using the determinant and its adjoint.

In this lesson, you will learn how to solve a 2 x 2 linear system using Cramer's rule

Practice test for Cramer's Rule 2 x 2 Linear System

This quiz will test your knowledge of how to find a solution for a linear system in two variables using Cramer's Rule.

In this lesson, we will look at some harder examples of solving linear systems with Cramer's Rule.

Practice test for solving a three variable linear system using Cramer's Rule.

This quiz will test your knowledge of how to find the solution for a linear system in three variables using Cramer's Rule.

Final Exam for the Matrix Algebra Course

Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Provides a solid foundation in matrix operations and techniques, which are essential for success in a linear algebra course
Covers solving linear systems using Gaussian and Gauss-Jordan elimination, which are fundamental techniques in linear algebra
Explores determinants and their applications, including finding the area of a triangle and testing for collinearity, which are useful in various mathematical contexts
Includes practice tests and quizzes for each lesson, allowing learners to assess their understanding and reinforce their skills
Focuses on the basics of matrices, so learners may need to seek additional resources for more advanced topics in linear algebra

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Create your own learning path. Save this course to your list so you can find it easily later.
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Reviews summary

Solid foundation in matrix algebra basics

According to students, this course provides a solid foundation in the basics of matrix algebra. Learners say it effectively covers key operations like addition, subtraction, and multiplication, as well as essential techniques for solving linear systems using methods such as Gaussian elimination and Cramer's rule. The explanations are often described as clear and easy to follow, making complex topics accessible. The inclusion of practice quizzes and tests is considered helpful for reinforcing understanding. While the course serves as a good introduction to entry-level linear algebra concepts, it primarily focuses on computational methods rather than theory and may be more easily understood with a basic algebra background.
Concentrates on 'how-to' calculations.
"This course teaches you the mechanics of matrix algebra and how to compute solutions."
"It's great for learning the calculations needed for fields like engineering or computer science."
"If you are looking for theoretical proofs or deeper mathematical theory, this course isn't the focus."
"The emphasis is on applying techniques to solve problems."
Quizzes reinforce understanding well.
"The practice tests after each section were invaluable for checking my progress and understanding."
"The quizzes helped solidify what I learned in the video lessons."
"Doing the exercises provided alongside the lessons made the concepts stick better."
"Found the assessment format helpful for testing my grasp of the procedures."
Teaches useful computational techniques.
"Learning different ways to solve linear systems using matrices was incredibly useful for my studies."
"The techniques for finding inverses, both by row reduction and adjoint, were well demonstrated."
"Cramer's Rule felt approachable and practical after completing this module."
"I now have a solid grasp on matrix multiplication needed for other subjects."
Explains core concepts well for beginners.
"The lessons on matrix operations were very straightforward and easy to follow."
"I finally understood Gaussian elimination thanks to the step-by-step approach presented."
"The instructor explained how to find determinants using Laplace expansion clearly."
"Complex topics were broken down into manageable parts that made sense."
May be challenging without prerequisites.
"I struggled a bit as my basic algebra skills weren't as strong as needed."
"Some concepts felt advanced if you're starting from an absolute zero math background."
"Be prepared to review some basic equation solving and algebraic manipulation first."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Matrix Algebra Explained with these activities:
Review Solving Linear Equations
Reinforce your understanding of solving linear equations, a fundamental skill needed for manipulating matrices and solving systems of equations.
Show steps
  • Review notes and examples of solving linear equations.
  • Practice solving various linear equations.
  • Check solutions and identify areas of weakness.
Review 'Introduction to Linear Algebra' by Gilbert Strang
Supplement your learning with a well-regarded textbook that offers clear explanations and numerous examples.
View Introduction to Linear Algebra. Sixth... on Amazon
Show steps
  • Read chapters relevant to the course syllabus.
  • Solve practice problems from the book.
  • Compare Strang's explanations with the course's.
Matrix Arithmetic Practice
Improve your speed and accuracy with matrix addition, subtraction, scalar multiplication, and matrix multiplication.
Show steps
  • Find online matrix calculators or practice worksheets.
  • Work through a set of matrix arithmetic problems.
  • Check answers and rework incorrect problems.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Create a Matrix Operations Cheat Sheet
Consolidate your knowledge by creating a reference sheet summarizing matrix operations, properties, and formulas.
Show steps
  • Gather all relevant formulas and properties.
  • Organize the information logically.
  • Design a visually appealing and easy-to-use cheat sheet.
Implement Gaussian Elimination in Code
Solidify your understanding of Gaussian elimination by implementing it in a programming language of your choice.
Show steps
  • Choose a programming language (e.g., Python, MATLAB).
  • Write code to perform row operations on a matrix.
  • Test the implementation with various matrices.
  • Debug and refine the code for accuracy.
Presentation on Applications of Determinants
Deepen your understanding of determinants by researching and presenting real-world applications.
Show steps
  • Research applications of determinants (e.g., cryptography, computer graphics).
  • Prepare a presentation outlining the applications.
  • Practice the presentation for clarity and conciseness.
Review 'Linear Algebra Done Right'
Expand your understanding of linear algebra concepts with a rigorous and theoretical approach.
View Linear Algebra Done Right (Undergraduate Texts... on Amazon
Show steps
  • Read selected chapters focusing on core concepts.
  • Work through examples and exercises.
  • Compare the book's approach to the course material.

Career center

Learners who complete Matrix Algebra Explained will develop knowledge and skills that may be useful to these careers:
Data Scientist
Data Scientists analyze complex data sets to extract meaningful insights and develop data driven solutions. As such, a strong grounding in the mathematical principles that underlie data analysis is essential. This Matrix Algebra Explained course provides a solid foundation in matrix operations, linear systems, and determinants, all of which are used extensively in machine learning algorithms and statistical modeling. Data scientists use techniques like Gaussian elimination for data preprocessing, matrix multiplication for feature engineering. Learning how to solve linear systems and calculate determinants, as taught in this course, helps you to understand the inner workings of many data science techniques.
See salaries and explore the career path for Data Scientist
Machine Learning Engineer
Machine Learning Engineers design, develop, and deploy machine learning models and algorithms. Matrix algebra is a foundational tool for machine learning, used in various algorithms such as linear regression, support vector machines, and neural networks. This Matrix Algebra Explained course provides a solid understanding of matrix operations, linear systems, and determinants, which are essential for understanding and implementing these algorithms. For any Machine Learning Engineer, the skills taught in this course are extremely useful for understanding core machine learning concepts.
See salaries and explore the career path for Machine Learning Engineer
Financial Engineer
Financial Engineers apply mathematical and computational methods to solve problems in finance. Matrix algebra is used extensively in portfolio optimization, risk management, and derivative pricing. This Matrix Algebra Explained course helps you learn how to solve linear systems, find determinants, and perform a variety of matrix operations. A Financial Engineer can use these techniques to build and analyze complex financial models. This course helps in developing a deep understanding of the mathematical tools used in the finance industry.
See salaries and explore the career path for Financial Engineer
Quantitative Analyst
Quantitative Analysts, often working in the financial sector, use mathematical and statistical models to analyze financial markets, assess risk, and develop trading strategies. Matrix algebra is a vital tool in this field. This course builds a foundation in solving linear systems, finding determinants, and performing matrix operations, skills that are crucial for building and understanding complex financial models. This course helps you learn how to apply techniques such as matrix inversion and Cramer's rule, which are used in portfolio optimization and risk management. For aspiring quantitative analysts, this Matrix Algebra Explained course helps to solidify your skills and knowledge.
See salaries and explore the career path for Quantitative Analyst
Game Developer
Game Developers design and create video games for various platforms. Matrix algebra is essential for game development, particularly in 3D graphics, physics simulations, and artificial intelligence. A game developer uses matrices to handle transformations, rotations, and scaling of game objects, as well as for solving systems of equations in physics engines. This Matrix Algebra Explained course helps build skills in matrix operations, linear systems, and determinants. Further, this course provides the quantitative knowledge necessary develop realistic and engaging game experiences.
See salaries and explore the career path for Game Developer
Computer Graphics Programmer
Computer Graphics Programmers create and implement algorithms for generating images and animations in software applications. Matrix algebra is fundamental to computer graphics as it is used for transformations such as scaling, rotation, and translation of objects in 2D and 3D space. This Matrix Algebra Explained course helps build a foundation in matrix manipulation, linear systems, and determinants. Computer graphics programmers use matrix transformations to manipulate objects and scenes. This course provides you with the knowledge and skills to develop graphical applications and simulations, and would be a great aid to any Computer Graphics Programmer.
See salaries and explore the career path for Computer Graphics Programmer
Operations Research Analyst
Operations Research Analysts use mathematical and analytical methods to solve complex decision-making problems. Matrix algebra is employed extensively in linear programming, optimization, and simulation. Operations Research Analysts apply the skills they develop in this course. This Matrix Algebra Explained course focuses on solving linear systems, finding determinants, and performing other matrix operations. This course helps develop the mathematical foundation necessary for success in operations research.
See salaries and explore the career path for Operations Research Analyst
Signal Processing Engineer
Signal Processing Engineers analyze and manipulate signals, such as audio, video, and sensor data. Matrix algebra is a critical tool in signal processing for tasks such as filtering, compression, and spectral analysis. Signal Processing Engineers can apply the skills developed in this course. This Matrix Algebra Explained course helps you learn about matrix operations, linear systems, and determinants. This course helps to provide a strong foundation in the mathematical techniques essential for signal processing.
See salaries and explore the career path for Signal Processing Engineer
Robotics Engineer
Robotics Engineers design, build, and program robots for various applications. Matrix algebra plays a crucial role in robotics, particularly in kinematics, dynamics, and control systems. The Robotics Engineer utilizes the skills developed in this course to design, model, and control robotic systems. This Matrix Algebra Explained course focuses on solving linear systems, finding determinants, and performing matrix operations. This course helps develop a strong mathematical foundation necessary for success in robotics engineering.
See salaries and explore the career path for Robotics Engineer
Image Processing Engineer
Image Processing Engineers develop algorithms and techniques for processing and analyzing images. Matrix algebra is a fundamental tool in image processing for tasks such as image filtering, enhancement, and compression. The Image Processing Engineer can leverage the skills developed in this course. This Matrix Algebra Explained course helps you learn matrix operations, linear systems, and determinants, principles that are necessary for many image processing techniques. This course would be useful to any Image Processing Engineer.
See salaries and explore the career path for Image Processing Engineer
Statistician
Statisticians collect, analyze, and interpret data to solve problems in various fields. Matrix algebra is used extensively in statistical modeling, multivariate analysis, and experimental design. For statisticians, this Matrix Algebra Explained course can be an extremely useful tool. This course helps you learn about matrix operations, linear systems, and determinants, which are essential for many statistical techniques. This course would strengthen a foundation in the mathematical tools used in statistics.
See salaries and explore the career path for Statistician
Econometrician
Econometricians use statistical methods to analyze economic data and test economic theories. Matrix algebra is a fundamental tool in econometrics, particularly in linear regression models and time series analysis. This Matrix Algebra Explained course will be useful. It will teach you how to solve linear systems and find determinants, and perform matrix operations. This course can help refine a skill set that is vital to econometric analysis and modeling.
See salaries and explore the career path for Econometrician
Data Analyst
Data Analysts collect, clean, and analyze data to identify trends and insights that can inform business decisions. While a Data Analyst role may not require the depth of knowledge of a Data Scientist, this Matrix Algebra Explained course may still be useful. It helps you deepen your understanding of the underlying mathematical principles behind common analytical techniques. Data analysis can involve the manipulation of data in a matrix format.
See salaries and explore the career path for Data Analyst
Surveyor
Surveyors measure and map land surfaces using various instruments and techniques. Matrix algebra is used in surveying to perform coordinate transformations, adjust measurements, and analyze survey data. For a surveyor, this Matrix Algebra Explained course may be useful. You solve linear systems and perform matrix operations to process field data. This course helps build a strong foundation in the mathematical techniques essential for surveying.
See salaries and explore the career path for Surveyor
Mathematics Teacher
Mathematics Teachers educate students in mathematical concepts and skills. While teaching mathematics, a Mathematics Teacher will likely need a deep understanding of the underlying principles of algebra. This Matrix Algebra Explained course can help solidify your knowledge of matrix algebra, including how to solve linear systems, find determinants, and perform matrix operations. These are all subjects that a Mathematics Teacher may need to introduce to their students.
See salaries and explore the career path for Mathematics Teacher

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Matrix Algebra Explained.
Introduction to Linear Algebra (Sixth Edition)
Save
Classic and widely used introduction to linear algebra. It provides a clear and intuitive explanation of the core concepts. It is particularly helpful for students who want to build a strong foundation in the subject. This book is often used as a textbook at many universities and valuable resource for self-study.
(中文) Introduction to Linear Algebra. Sixth...
Paperback
$$$$
Cover image
Linear Algebra Done Right
Save
Provides a more theoretical and abstract treatment of linear algebra. It is useful for students who want to deepen their understanding of the underlying concepts. While not strictly necessary for this introductory course, it provides a solid foundation for further study in linear algebra and related fields. It is commonly used as a textbook in advanced undergraduate and graduate courses.
Linear Algebra Done Right (Undergraduate Texts in...
Hardcover
$$
Linear Algebra Done Right (Undergraduate Texts in...
Kindle Edition
$$
Linear Algebra Done Right (Undergraduate Texts in...
Hardcover
$$
Linear Algebra Done Right (Undergraduate Texts in...
Paperback
$$$$
(Español) Aljebra lineala ondo egina
Paperback
$$

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Rating
4.8 Filled star Filled star Filled star Filled star Half star
Effort
8.5 total hours
Via
Udemy
Instructor
John Greene, M.A.
Language
English
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Provides a solid foundation in matrix operations and techniques, which are essential for success in a linear algebra course
Covers solving linear systems using Gaussian and Gauss-Jordan elimination, which are fundamental techniques in linear algebra
Explores determinants and their applications, including finding the area of a triangle and testing for collinearity, which are useful in various mathematical contexts
Includes practice tests and quizzes for each lesson, allowing learners to assess their understanding and reinforce their skills
Focuses on the basics of matrices, so learners may need to seek additional resources for more advanced topics in linear algebra
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