About This Chapter
Who's It For?
Anyone who needs help learning or mastering matrices in linear algebra will benefit from the lessons in this chapter. There is no faster or easier way to learn matrices in linear algebra. Among those who would benefit are:
- Students who have fallen behind in understanding working with matrices in linear algebra
- 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 matrices in linear algebra
- 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 Matrices in Linear Algebra 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 Matrices in Linear Algebra chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any matrices in linear algebra question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in a matrices in linear algebra unit of a standard algebra course. Topics covered include:
- The definition of a matrix
- How to solve inverse matrices
- Using Gaussian elimination to solve linear systems
- Cramer's Rule and inconsistent systems
- Writing an augmented matrix for linear systems
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. Square Matrix: Definition & Concept
A square matrix is a special type of matrix with an equal number of rows and columns. Learn more about square matrices in this lesson, including how to add and multiply them. Then, test your understanding with a short quiz.
3. 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.
4. 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.
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.
6. 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.
7. 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.
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.
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.
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.
11. 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.
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