About This Chapter
Matrices and Determinants in Algebra - Chapter Summary
The lessons in this chapter will help you understand what a matrix is, including augmented, equal and inverse matrices, and how to perform operations with them. Our instructors explain concepts such as Gaussian elimination and Cramer's rule and show you how to utilize them. You'll learn to take the determinant of a matrix and how to evaluate higher-order determinants. After completing these lessons, you should be ready to:
- Define a matrix
- Perform matrix row operations
- Understand math operations with matrices
- Solve inverse matrices
- Utilize Gaussian and Gauss-Jordan elimination
- Use determinants to solve systems of linear equations in two and three variables
All our lessons include short multiple-choice quizzes that let you gauge your learning and practice your test-taking skills. If you need to review a particular concept, the timeline in the lessons makes it simple to go back and find the proper section. Written transcripts of all the lessons are included, and you can conclude your study of this topic with a chapter exam.
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 within the Accuplacer College Level Math Test: Practice & Study Guide course
- Operations with Basic Algebraic Expressions
- Arithmetic with Rational Expressions
- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Graphs of Algebraic Functions
- Complex and Imaginary Numbers
- Notation, Sequences & Series
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations