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Ch 9: Overview of Matrices & Determinants

About This Chapter

Watch the fun video lessons in this chapter to ensure you fully grasp matrices and determinants. Take the multiple-choice quizzes accompanying the lessons to deepen your understanding and enhance your preparations for a test covering this subject.

Overview of Matrices & Determinants - Chapter Summary

These entertaining video lessons provide a comprehensive overview of matrices and determinants. Developed by expert instructors, the lessons help you better understand how to perform matrix row operations, solve inverse matrices and linear systems, evaluate higher-order determinants and more. Once you've completed this chapter, you should be able to:

  • Define a matrix and write an augmented matrix for a linear system
  • Understand matrix notation, equal matrices and math operations with matrices
  • Describe when to use Gaussian elimination to solve inconsistent and dependent systems
  • Exhibit an understanding of multiplicative inverses of matrices
  • Take a determinant of a matrix
  • Solve systems of linear equations in two and three variables using determinants
  • Use Cramer's Rule with dependent and inconsistent systems

All lessons in this chapter are available as short videos and full transcripts. Videos average about 8 minutes each and feature clickable timelines you can use to skip to key topics within the lessons. Full transcripts allow you to read the lessons as texts and can be printed or viewed online. With each lesson is a short quiz designed to assess your knowledge of the concepts it covers. A chapter exam is also available to gauge your overall understanding of matrices and determinants.

14 Lessons in Chapter 9: Overview of Matrices & Determinants
Test your knowledge with a 30-question chapter practice test
What is a Matrix?

1. What is a Matrix?

As math gets more and more complicated and there become more and more numbers flying around, it becomes really handy to put all these numbers in a nice organized grid... hello matrices! Learn about what they are and why there are used.

How to Write an Augmented Matrix for a Linear System

2. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

How to Perform Matrix Row Operations

3. How to Perform Matrix Row Operations

Watch this video lesson to learn how easy it is to perform row operations on a matrix. Learn how to perform the three basic operations easily and quickly.

Matrix Notation, Equal Matrices & Math Operations with Matrices

4. Matrix Notation, Equal Matrices & Math Operations with Matrices

Watch this video lesson to learn about the basics of matrices and what kinds of math operations you can do with them. Also learn how to determine whether two matrices are the same or not.

How to Solve Inverse Matrices

5. How to Solve Inverse Matrices

Watch this video lesson to learn what kinds of matrix operations you can take to find the inverse of a matrix. Also learn why matrix inverses are useful.

How to Solve Linear Systems Using Gaussian Elimination

6. How to Solve Linear Systems Using Gaussian Elimination

Watch this video lesson to learn an easy way to solve a system of equations that involves manipulating a matrix. Learn the kinds of easy matrix manipulations that are needed to solve any system of equations.

How to Solve Linear Systems Using Gauss-Jordan Elimination

7. How to Solve Linear Systems Using Gauss-Jordan Elimination

You will come across simple linear systems and more complex ones as you progress in math. Watch this video lesson to learn how you can use Gauss-Jordan elimination to help you solve these linear systems.

Inconsistent and Dependent Systems: Using Gaussian Elimination

8. Inconsistent and Dependent Systems: Using Gaussian Elimination

Watch this video lesson to learn whether or not you can use Gaussian elimination to solve inconsistent and dependent systems. Also, learn whether there is another way to find solutions of these systems.

Multiplicative Inverses of Matrices and Matrix Equations

9. Multiplicative Inverses of Matrices and Matrix Equations

Watch this video lesson to learn about another method you can use to solve a matrix problem if you are given the inverse of the matrix. You will also learn the identifying mark of the multiplicative inverse of a matrix.

How to Take a Determinant of a Matrix

10. How to Take a Determinant of a Matrix

Matrices are incredibly powerful and can help you do all sorts of things, but one of the most basic (and surprisingly helpful) operations you can perform on one is to take its determinant. Learn how to do that here!

Solving Systems of Linear Equations in Two Variables Using Determinants

11. Solving Systems of Linear Equations in Two Variables Using Determinants

Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.

Solving Systems of Linear Equations in Three Variables Using Determinants

12. Solving Systems of Linear Equations in Three Variables Using Determinants

Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.

Using Cramer's Rule with Inconsistent and Dependent Systems

13. Using Cramer's Rule with Inconsistent and Dependent Systems

Watch this video lesson, and you will see what happens when we use Cramer's Rule with inconsistent and dependent systems. You will see what kind of result you will always get when you try to use Cramer's Rule.

How to Evaluate Higher-Order Determinants in Algebra

14. How to Evaluate Higher-Order Determinants in Algebra

Watch this video lesson to learn the rules for taking the determinant of any size matrix. Learn the kind of matrix that you need before you can take the determinant. Watch as the pattern of the determinant takes shape.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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