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Ch 4: Solving Matrices & Determinants

About This Chapter

Let us help you boost your understanding of how to solve mathematical equations using determinants and matrices. These lessons and quizzes can be used to help you earn the best score you can on an upcoming test or homework assignment.

Solving Matrices & Determinants - Chapter Summary

In this chapter, you will learn about systems of equations and the many types of matrices that exist in the mathematical world. Our instructors will define reduced row-echelon forms and explain how to take a determinant of a matrix. Your study will continue with steps to solve systems of linear equations in two and three variables using determinants.

As you progress through the chapter, you will review matrix notation, and learn how to use rules to take the determinant of any size matrix. These lessons will teach you how to:

  • Differentiate between and identify the different kinds of matrices
  • Define reduced row-echelon form
  • Take the determinant of a matrix
  • Solve systems of linear equations using Cramer's Rule
  • Explain the math operations you can do with matrices
  • Use rules to work with higher-order determinants
  • Solve inverse matrices
  • Give examples of adjugate matrices

Use our chapter tests and lesson quizzes to gauge how well you understand the subject matter and where you may want to focus additional study. These materials are designed by professional instructors to ensure your learning experience is easy and engaging. If you need help as you work through the lessons, contact one of our instructors for assistance. All our lessons and quizzes are available to you anytime, and you can print the quizzes and transcripts for offline study.

10 Lessons in Chapter 4: Solving Matrices & Determinants
Test your knowledge with a 30-question chapter practice test
What is a System of Equations?

1. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

Types of Matrices: Definition & Differences

2. Types of Matrices: Definition & Differences

Matrices are rectangular arrays of numbers arranged in the form of rows and columns. In this lesson, you will explore the various types of matrices with examples of each.

Reduced Row-Echelon Form: Definition & Examples

3. Reduced Row-Echelon Form: Definition & Examples

In this lesson, we'll look at one of the most useful forms of a matrix: the reduced row-echelon form. We'll review the definition of reduced row-echelon form and look at several examples.

How to Take a Determinant of a Matrix

4. 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

5. 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

6. 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.

Matrix Notation, Equal Matrices & Math Operations with Matrices

7. 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 Evaluate Higher-Order Determinants in Algebra

8. 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.

How to Solve Inverse Matrices

9. 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.

Adjugate Matrix: Definition, Formation & Example

10. Adjugate Matrix: Definition, Formation & Example

In this lesson we'll calculate the adjugate matrix. This will require finding minors, determinants, and transposes. All of these steps will be carefully explained with an example.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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