# Ch 16: ACT Math - Matrices: Tutoring Solution

### About This Chapter

## How it works:

- Begin your ACT review or other math preparation 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 ACT prep tutoring solution will benefit any student who is trying to learn matrices and earn acceptable scores. This resource can help students including those who:

- Struggle with understanding how to take a determinant of a matrix or any other matrices topic
- Have limited time for studying
- Want a cost effective way to supplement their ACT preparation
- Prefer learning ACT topics visually
- Find themselves struggling with the matrices portion of the review
- Cope with ADD or ADHD
- Want to get ahead in their ACT preparation
- Don't have access to ACT review materials

## Why it works:

**Engaging Tutors:**We make learning about matrices 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 ACT prep tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Complete your matrices review 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:

- Review what a matrix is.
- Learn how to take a determinant of a matrix.

### 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. 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.

### 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 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. Finding the Inverse of a 3x3 Matrix

Do you know what the inverse of a 3x3 matrix is and how to find it? This lesson goes over these and related concepts necessary for finding the inverse of a sample 3x3 matrix.

### 7. How to Find the Inverse of a 4x4 Matrix

This lesson defines a matrix and some related terms, as well as outlining the rules and guidelines for working with matrices. Once these terms are defined, we will discuss how to find the inverse of a 4x4 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. 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.

### 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!

### 13. Finding the Determinant of a 3x3 Matrix

What is a determinant and how do you find it? This lesson explains what a determinant is and shows you a step-by-step process for finding the determinant of a 3 x 3 matrix.

### 14. How to Find the Determinant of a 4x4 Matrix

Finding the determinant of a matrix helps you do many other useful things with that matrix. This lesson shows step by step how to find a determinant for a 4x4 matrix. The process used is applicable to a square matrix of any size larger than 2x2.

### 15. 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.

### 16. 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.

### 17. 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.

### 18. 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.

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### Other Chapters

Other chapters within the ACT Prep: Tutoring Solution course

- ACT - About the Test: Tutoring Solution
- ACT English - Section Overview: Tutoring Solution
- ACT English - Punctuation: Tutoring Solution
- ACT English - Grammar and Usage: Tutoring Solution
- ACT English - Sentence Structure: Tutoring Solution
- ACT English - Rhetorical Strategy: Tutoring Solution
- ACT English - Organization: Tutoring Solution
- ACT English - Style: Tutoring Solution
- ACT Math - Overview: Tutoring Solution
- ACT Math - Pre-Algebra: Tutoring Solution
- ACT Math - Algebraic Expressions: Tutoring Solution
- ACT Math - Radicals: Tutoring Solution
- ACT Math - Linear Equations: Tutoring Solution
- ACT Math - Functions: Tutoring Solution
- ACT Math - Absolute Value: Tutoring Solution
- ACT Math - Inequalities: Tutoring Solution
- ACT Math - Probability: Tutoring Solution
- ACT Math - Data and Statistics: Tutoring Solution
- ACT Math - Exponents: Tutoring Solution
- ACT Math - Polynomials and Quadratics: Tutoring Solution
- ACT Math - Rational Equations: Tutoring Solution
- ACT Math - Sequences: Tutoring Solution
- ACT Math - Complex Numbers: Tutoring Solution
- ACT Math - Exponentials and Logarithms: Tutoring Solution
- ACT Math - Coordinate Geometry: Tutoring Solution
- ACT Math - Conic Sections: Tutoring Solution
- ACT Math - Triangles: Tutoring Solution
- ACT Math - Plane Geometry: Tutoring Solution
- ACT Math - Logic in Mathematics: Tutoring Solution
- ACT Math - Trigonometry: Tutoring Solution
- ACT Science Reasoning - Overview: Tutoring Solution
- ACT Science Reasoning - Fundamentals: Tutoring Solution
- ACT Reading - Overview: Tutoring Solution
- ACT Reading - Question Types: Tutoring Solution
- ACT Reading - Understanding Passages: Tutoring Solution
- ACT Reading - Literary Terms: Tutoring Solution
- ACT Reading - Practice: Tutoring Solution
- ACT Writing - Overview: Tutoring Solution
- ACT Writing - Essay Skills: Tutoring Solution
- ACT Writing - Essay Parts: Tutoring Solution
- ACT Writing - Planning: Tutoring Solution
- ACT Writing - Advanced Skills: Tutoring Solution