Ch 26: Vectors, Matrices and Determinants: Help and Review

About This Chapter

The Vectors, Matrices and Determinants chapter of this High School Precalculus Help and Review course is the simplest way to master vectors, matrices and determinants. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of vectors, matrices and determinants.

Who's it for?

Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:

  • Students who have fallen behind in understanding vectors in the plane or working with matrices and determinants
  • Students who struggle with learning disabilities or learning differences, including autism and ADHD
  • Students who prefer multiple ways of learning math (visual or auditory)
  • Students who have missed class time and need to catch up
  • Students who need an efficient way to learn about vectors, matrices and determinants
  • Students who struggle to understand their teachers
  • Students who attend schools without extra math learning resources

How it works:

  • Find videos in our course that cover what you need to learn or review.
  • Press play and watch the video lesson.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Verify you're ready by completing the Vectors, Matrices and Determinants chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Vectors, Matrices and Determinants chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any vector, matrix or determinant question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll find answers to questions including:

  • How do I add, subtract and multiply by scalars on vectors in the plane?
  • How do I use matrix notation?
  • What do I do to solve linear systems with matrices?
  • How do I take a determinant of a matrix?

19 Lessons in Chapter 26: Vectors, Matrices and Determinants: Help and Review
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.

How to Solve Linear Systems Using Gaussian Elimination

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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.

Reduced Row-Echelon Form: Definition & Examples

17. 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.

Divergence Theorem: Definition, Applications & Examples

18. Divergence Theorem: Definition, Applications & Examples

Solids, liquids and gases can all flow. Calculating the rate of flow through a surface is often made simpler by using the divergence theorem. In this lesson we explore how this is done.

Linear Independence: Definition & Examples

19. Linear Independence: Definition & Examples

Do you know what linear independence is and when it is used? This lesson gives a definition of linear independence, how to test for it, and also goes over some examples of the testing process.

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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