# Ch 10: Algebra II - Matrices and Determinants: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school algebra material will benefit from taking this course. There is no faster or easier way to learn high school algebra. Among those who would benefit are:

- Students who have fallen behind in understanding how to perform matrix row operations or working with taking a determinant of a matrix
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about determinants and matrices
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Algebra II: Matrices and Determinants chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Algebra II: Matrices and Determinants chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any matrices and determinants question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in an Algebra II: Matrices and Determinants unit of a standard high school algebra II course. Topics covered include:

- Matrix notation
- Inconsistent and dependent systems
- Multiplicative inverses of matrices and matrix equations
- Solving linear systems using Gaussian elimination method
- Evaluating higher-order determinants in algebra

### 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.

### Earning College Credit

Did you know… We have over 160 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 High School Algebra II: Help and Review course

- Algebra II - Basic Arithmetic Review: Help and Review
- Algebra II - Algebraic Expressions: Help & Review
- Algebra II - Real Numbers: Help and Review
- Algebra II - Complex and Imaginary Numbers Review: Help and Review
- Exponents & Exponential Expressions in Algebra: Help & Review
- Algebra II - Properties of Functions Review: Help and Review
- Algebra II - Linear Equations Review: Help and Review
- Algebra II - Systems of Linear Equations: Help and Review
- Algebra II - Inequalities Review: Help and Review
- Algebra II - Absolute Value Review: Help and Review
- Algebra II - Polynomials: Help and Review
- Algebra II - Factoring: Help and Review
- Algebra II Quadratic Equations: Help and Review
- Algebra II - Rational Expressions: Help and Review
- Algebra II - Graphing and Functions: Help and Review
- Algebra II - Roots and Radical Expressions Review: Help and Review
- Algebra II - Quadratic Equations: Help and Review
- Algebra II - Exponential and Logarithmic Functions: Help and Review
- Algebra II - Conic Sections: Help and Review
- Algebra II - Sequences and Series: Help and Review
- Algebra II - Sets: Help and Review
- Algebra II - Combinatorics: Help and Review
- Algebra II Ratios & Proportions: Help & Review
- Algebra II - Statistics: Help and Review
- Algebra II - Trigonometry: Help and Review