Ch 11: Matrices Overview

About This Chapter

For a quick review on mathematical matrices, use the engaging text and video lessons in this chapter. Each lesson explains a key matrix topic, while the interactive quizzes provide you with practice questions that can help you prepare for an exam or homework assignment.

Matrices Overview - Chapter Summary

Get a refresher on the uses of matrices in mathematics with this chapter. Begin with an overview of what matrices are and how they are used in mathematical functions. Once you understand the basics, you can explore how the determinants of a matrix can be used to solve linear functions of different variables. Matrix recurrence relations and their usefulness in modeling populations and sequences is also explained. After completing this set of lessons, you'll be able to:

  • Define a matrix and differentiate between types of matrices
  • Solve inverse matrices
  • Identify the multiplative inverse of a matrix equation
  • Explain the properties of bianary and permutation matrices
  • Discuss communication and dominance matrices
  • Show how to generate sequences and model population using matrices
  • Solve systems of linear equations using determinants

These lessons use either an engaging video or text format to break complex topics down into interesting, easy-to-understand material. The self-assessment quizzes, included with each lesson, help you identify any topics you found confusing or would like to know more about. The Dashboard feature of your account page tracks your progress in every lesson, no matter where you login.

9 Lessons in Chapter 11: Matrices Overview
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.

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.

How to Solve Inverse Matrices

3. 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.

Multiplicative Inverses of Matrices and Matrix Equations

4. 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

5. 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

6. 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

7. 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 the Matrix Recurrence Relation to Generate Sequences

8. Using the Matrix Recurrence Relation to Generate Sequences

In this lesson we explore how to use matrix multiplication and an initial condition to produce all the numbers in a recursive sequence. The example set of numbers is the Fibonacci sequence.

Using the Matrix Recurrence Relation to Model Populations

9. Using the Matrix Recurrence Relation to Model Populations

Modeling populations is both fascinating and relevant. If we can predict how a population will change, we can make better use of resources. In this lesson, we use a matrix recurrence relation to model the population of a school.

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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