# Ch 4: McDougal Littell Algebra 2 Chapter 4: Matrices and Determinants

### About This Chapter

## How it works:

- Identify the lessons in the McDougal Littell Algebra 2 Matrices and Determinants chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the matrices and determinants topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- Matrix notation
- Equal matrices
- Math operations with matrices
- Matrix row operations
- Determinants of matrices
- Cramer's rule
- Inverse matrices
- Multiplicative inverses of matrices

*McDougal Littell Algebra 2 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. What is a Matrix?

A matrix is an array of numbers enclosed in brackets that represents a system of equations. Explore matrices and the parts of a matrix and learn how to add, subtract, and multiply matrices.

### 2. Matrix Notation, Equal Matrices & Math Operations with Matrices

Matrices are rectangular arrays of numbers that can be used to solve systems of equations. Review how to identify proper matrix notation, understand when matrices are equal, and learn how to add, subtract, and multiply them.

### 3. How to Perform Matrix Row Operations

A matrix is known as a bunch of numbers arranged in rows and columns and is useful to maths in various ways. Learn more about describing a matrix, modifying them through addition, multiplication or switching and correct notation.

### 4. How to Take a Determinant of a Matrix

The determinant is a simple but unique operation you can perform with a matrix. Learn how to solve for the determinant based on the size of the matrix, and study explanations of each type of matrix to expand your math vocabulary.

### 5. Using Cramer's Rule with Inconsistent and Dependent Systems

Cramer's rule is a very acute way to solve linear systems for its various variables. Learn more about using Cramer's rule with inconsistent and dependent systems.

### 6. Solving Systems of Linear Equations in Two Variables Using Determinants

A system of linear equations includes two or more equations made up of two or more variables and no exponents. This lesson demonstrates how to solve these equations using Cramer's rule to help find the determinants.

### 7. Solving Systems of Linear Equations in Three Variables Using Determinants

Cramer's rule can be used to solve systems of linear equations in three variables. Learn about the linear system in three variables, the detailed explanation of Cramer's rule, and finding determinants to solve such equations.

### 8. How to Solve Inverse Matrices

An inverse matrix can be multiplied with the original matrix to determine the identity matrix of an equation. Learn about the inverse matrix, the identity matrix, and how to use matrix operations to solve inverse matrices.

### 9. Multiplicative Inverses of Matrices and Matrix Equations

The multiplicative inverse of matrices states that matrix identify can be determined by multiplying a matrix with its multiplicative inverse. Learn how to use the matrix multiplicative inverse to solve matrix equations through a series of examples.

### Earning College Credit

Did you know… We have over 220 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

### Other Chapters

Other chapters within the McDougal Littell Algebra 2: Online Textbook Help course

- McDougal Littell Algebra 2 Chapter 1: Equations and Inequalities
- McDougal Littell Algebra 2 Chapter 2: Linear Equations and Functions
- McDougal Littell Algebra 2 Chapter 3: Systems of Linear Equations and Inequalities
- McDougal Littell Algebra 2 Chapter 5: Quadratic Functions
- McDougal Littell Algebra 2 Chapter 6: Polynomials and Polynomial Functions
- McDougal Littell Algebra 2 Chapter 7: Powers, Roots, and Radicals
- McDougal Littell Algebra 2 Chapter 8: Exponential and Logarithmic Functions
- McDougal Littell Algebra 2 Chapter 9: Rational Equations and Functions
- McDougal Littell Algebra 2 Chapter 10: Quadratic Relations and Conic Sections
- McDougal Littell Algebra 2 Chapter 11: Sequences and Series
- McDougal Littell Algebra 2 Chapter 12: Probability and Statistics
- McDougal Littell Algebra 2 Chapter 13: Trigonometric Ratios and Functions
- McDougal Littell Algebra 2 Chapter 14: Trigonometric Graphs, Identities, and Equations