About This Chapter
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.
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.
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.
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.
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.
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!
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.
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.
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.
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.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
- Population & Samples
- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
- Correlation & Causation in Math
- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Graphs & Networks
- Paths & Circuits
- Problem Solving With Networks
- Geometric Solids
- Measurement & Trigonometry
- Spherical Geometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
- VCE Further Mathematics Flashcards