Ch 15: CEOE Advanced Math: Vectors, Matrices & Determinants

About This Chapter

These lessons have been composed to help you improve your understanding of operations with vectors and matrices as well as how to find the determinant of a matrix and solve systems of linear equations. Use these lessons to prepare for related exam questions on the CEOE Advanced Mathematics exam.

CEOE Advanced Math: Vectors, Matrices & Determinants - Chapter Summary

This chapter's lessons will aid in your review of vectors, matrices and systems of linear equations. Our expert instructors will explain these topics and demonstrate example problems to help you improve your abilities in:

  • Completing operations with vectors in a plane
  • Using dot products of vectors to solve problems
  • Writing and augmenting matrices for linear systems
  • Performing matrix row operations and other math operations on matrices
  • Solving inverse matrices
  • Taking determinants of a matrix
  • Solving systems of linear equations
  • Evaluating higher-order determinants

Each lesson video is accompanied by a lesson transcript and lesson quiz. Read the lesson transcripts to reinforce your retention of the information and take the lesson quizzes to test your understanding. Review your quiz results and discover the topics you don't understand.

CEOE Advanced Math: Vectors, Matrices & Determinants Objectives

The Certification Examinations for Oklahoma Educators (CEOE) Advanced Mathematics exam is a computer-based test. It is composed of 80 multiple-choice questions and one constructed-response item which you will be asked to complete in a four-hour testing session. Of the material covered in this exam, 27% is in the subarea about relations, functions and algebra. Some of these questions may test your abilities solving problems with vectors, matrices and determinants.

12 Lessons in Chapter 15: CEOE Advanced Math: Vectors, Matrices & Determinants
Test your knowledge with a 30-question chapter practice test
Performing Operations on Vectors in the Plane

1. Performing Operations on Vectors in the Plane

After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.

The Dot Product of Vectors: Definition & Application

2. The Dot Product of Vectors: Definition & Application

After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.

What is a Matrix?

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.

How to Evaluate Higher-Order Determinants in Algebra

12. 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

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

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

Support