# Ch 16: ACT Math: Matrices

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### About This Chapter

## ACT Math: Matrices - Chapter Summary

Matrices are a fundamental aspect of the linear algebra branch of math. In this chapter, review the following basic information through our motivating videos:

- Definition of matrix
- How and why matrices are used
- Parts of a matrix: rows, columns and brackets
- Adding, subtracting and multiplying matrices
- Taking determinants of matrices

Go over all of the information about matrices so that you can demonstrate proficiency on the ACT math test. View concise examples of matrices in the lessons, and take the follow-up quizzes to see how you're doing.

### ACT Math Objectives

The ACT test speaks to the three mathematical areas of algebra, geometry and trigonometry. The exam considers algebra as three levels: pre-, elementary and intermediate. Overall, the algebra section involves 55% of the 60-question test. Our review lessons, followed by self-assessment quizzes, will help you revisit the key concepts necessary for the ACT. The test's pre-algebra questions assume a base built upon an understanding of fundamental linear algebra skills. The exam then checks for more in-depth understanding of the intermediate skills directly related to matrices.

You'll have 60 minutes to complete 60 multiple-choice math problems. You can complete all of the questions without the use of calculators. However, you'll be able to use certain approved models of calculators, if you wish to do so. Check with the ACT student site for details concerning calculator use.

Your score report will include four scores for the math portion of the test: an overall score on all 60 questions and sub-scores for pre-algebra/elementary algebra, intermediate algebra/coordinate geometry and plane geometry/trigonometry.

### 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. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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!

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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: Practice & Study Guide course

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