# Ch 10: Algebra II: Matrices and Determinants

Watch online math video lessons and learn about matrix notation, augmented matrices, Cramer's rule and more. These lessons are just a portion of our high school Algebra II course materials.

## Algebra II: Matrices and Determinants - Chapter Summary and Learning Objectives

If you're having a hard time wrapping your head around matrices, this chapter is for you. Our instructors can show you how these sets of numbers are used to solve systems of equations in linear algebra, making matrices a useful tool in a variety of fields, including computer programming. Watch the videos to learn how to perform basic arithmetic operations with matrices and work with their determinants. By the end of this chapter, you should be able to:

• Write matrices and perform matrix row operations
• Add, subtract and multiply matrices and find their inverses
• Apply Gaussian and Gauss-Jordan elimination methods
• Find a matrix's determinant and use it to solve a linear system

Video Objectives
What Is a Matrix? Identify the components of a matrix and explore its uses to solve systems of equations. Find out how to add, subtract and multiply matrices.
How to Write an Augmented Matrix for a Linear System Learn the steps involved in writing an augmented matrix for a linear system.
How to Perform Matrix Row Operations Understand how to perform basic matrix row operations.
Matrix Notation, Equal Matrices & Math Operations with Matrices Learn what equal matrices are and demonstrate the proper use of matrix notation.
How to Solve Inverse Matrices Find out what it takes to identify and solve inverse matrices.
How to Solve Linear Systems Using Gaussian Elimination Understand how to solve linear systems using matrices and Gaussian elimination.
How to Solve Linear Systems Using Gauss-Jordan Elimination Explain how to use matrices and Gauss-Jordan elimination to solve linear systems.
Inconsistent and Dependent Systems: Using Gaussian Elimination Use Gaussian elimination to solve linear systems with more variables than equations or linear systems without unique solutions.
Multiplicative Inverses of Matrices and Matrix Equations Find the multiplicative inverse of a square matrix. Learn how inverses can be used to solve matrix equations and encode and decode messages.
How to Take a Determinant of a Matrix Identify square matrices and discover methods for finding their determinants.
Solving Systems of Linear Equations in Two Variables Using Determinants Find out how to evaluate a second-order determinant. Use Cramer's rule to solve a system of linear equations in two variables.
Solving Systems of Linear Equations in Three Variables Using Determinants Evaluate a third-order determinant. Understand the steps required to solve a system of linear equations in three variables using Cramer's rule.
Using Cramer's Rule with Inconsistent and Dependent Systems Identify linear systems with dependent equations as well as inconsistent systems using determinants.
How to Evaluate Higher-Order Determinants in Algebra Explain the processes involved in evaluating higher-order determinants.

14 Lessons in Chapter 10: Algebra II: Matrices and Determinants
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

### 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.