About This Chapter
Matrices in Algebra - Chapter Summary
In this chapter, our instructors explain what matrices are and the kinds of math operations you can do with them. You will learn about taking the inverse of a matrix and why this is useful. The concepts of matrix exponentials and how to find the logarithm of a matrix will also be introduced.
Your study continues with a discussion about how to take the determinant of a matrix and why this is one of the most basic and helpful operations. Matrix manipulations and solving linear equations in two and three variables using determinants are also introduced. After you have finished these lessons, you should be able to:
- Perform math operations using matrices
- Solve inverse matrices
- Give an example of a matrix exponential and a logarithm of a matrix
- Take the determinant of a matrix
- Calculate systems of equations using easy matrix manipulations
- Use determinants to find the solution of a linear system with two variables
- Utilize Cramer's Rule in your solutions
Our lessons and quizzes are created by professional instructors to ensure learning is easy and engaging. Use the quizzes and chapter tests to gauge how well you understand the material and what needs to be reviewed further. If you need to re-watch just a portion of one of the videos, use the video tabs in the Timeline to jump to the section you'd like to review. Our lessons and quizzes are mobile-friendly and accessible to you at any time.
1. 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.
2. 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.
3. 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!
4. 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.
5. 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.
6. 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.
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