About This Chapter
Matrices and Absolute Value
Join us as we enter The Matrix. Well, not exactly the sci-fi alternate reality, but in this lesson series, you'll discover the world of matrices that exists in mathematics - which can be just as fun and exciting as a Friday night trip to the movies!
In these video lessons, you'll learn how matrices are used to organize numbers. Essentially, a matrix is a grid that's divided into rows and columns, and they are useful for organizing a large amount of numbers. You could have a simple 2x2 matrix or a complex matrix with many rows and columns. After learning the basics of matrices, you'll learn how to solve systems of equations with multiple variables and learn how to take the determinant of a matrix.
Next, you'll explore absolute values. Absolute values determine the magnitude of a number or how 'large' it is. In other words, absolute values don't care if a number is positive or negative; they only care about how far a number is away from 0. As you become familiar with the rules of absolute values and how they can be applied to real life, you'll learn how to evaluate, graph and solve absolute value equations. Don't get frustrated though, because with absolute values, it's important to stay positive! Our easy-to-follow lessons will make things very accessible, and simple to learn. Plus, our instructors provide sample problems and examples along the way to ensure you understand the material completely.
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 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!
3. What is an Absolute Value?
When we're talking and comparing numbers, we often don't care whether its positive or negative, just how big it is. This is often called the magnitude of a number and we find it by taking the absolute value. Learn all about it here!
4. How to Evaluate Absolute Value Expressions
Substituting values into absolute values doesn't have to be too hard, but it can be if you're given deceiving beginning information. See if you're up to it by checking out this video!
5. How to Solve an Absolute Value Equation
Once you get familiar with any new operation, the next step in any algebra class is to learn how to solve equations with that operation in them. Absolute values are no different. Solve absolute value equations here!
6. Solving Absolute Value Practice Problems
There are many easy mistakes to make when solving absolute value equations. Learn how to avoid those mistakes here by working on examples of absolute value equations with operations on the inside and the outside of the absolute value.
7. How to Graph an Absolute Value and Do Transformations
Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. As well as teaching you how to graph absolute values, this video will focus on a specific group of transformations called translations. Learn all about what that means here!
8. Graphing Absolute Value Equations: Dilations & Reflections
Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing! In this lesson, you'll practice different transformations of absolute value graphs.
9. Practice Problem Set for Matrices and Absolute Values
If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.
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Other chapters within the Math 101: College Algebra course
- Foundations of Linear Equations
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101