# Ch 4: Matrices in Linear Algebra: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other linear algebra work.
- Identify the matrices concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our Linear Algebra Tutoring Solution will benefit any student who is trying to learn matrices in linear algebra and earn better grades. This resource can help students including those who:

- Struggle with understanding the matrix, performing matrix row operations, solving linear systems or any other matrices in linear algebra topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their matrices in linear algebra unit
- Cope with ADD or ADHD
- Want to get ahead in linear algebra
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning matrices in linear algebra simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn matrices in linear algebra on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning objectives

- Define the matrix and square matrix.
- Write an augmented matrix for a linear system.
- Understand matrix notation, equal matrices and math operations with matrices.
- Perform matrix row operations and solve inverse matrices.
- Study multiplication inverses of matrices and matrix equations.
- Solve linear systems using Gaussian elimination and Gauss-Jordan elimination.
- Explore inconsistent and dependent systems.
- Understand how to use Cramer's Rule with inconsistent and dependent 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. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 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 Linear Algebra: Tutoring Solution course