# Ch 18: High School Algebra: Matrices and Absolute Value

### About This Chapter

## Matrices and Absolute Value - Chapter Summary and Learning Objectives

Matrices are number grids that serve as the basis for linear mathematics. Absolute values are how far a number is from zero no matter if the number is positive or negative. Our instructors show you how matrices are used in mathematics as well as explain how absolute values are important. In addition to our video lessons, you will find quizzes that help you determine your progress for understanding matrix and absolute value concepts. This chapter is designed to teach you how to:

- Take a determinant of a 2x2 matrix
- Graph an absolute value
- Evaluate complicated absolute value equations
- Explain why matrices and absolute values are useful

Video | Objective |
---|---|

What is a Matrix? | Introduce what a matrix is and why they are useful. |

How to Take a Determinant of a Matrix | Learn how to take a determinant of a 2x2 matrix. |

What is an Absolute Value? | Introduce what an absolute value is and why they are useful. |

How to Evaluate Absolute Value Expressions | Learn how to evaluate complicated absolute value equations. |

How to Solve an Absolute Value Equation | Learn how to solve an absolute value equation. |

Solving Absolute Value Practice Problems | Get practice solving absolute values. |

How to Graph an Absolute Value and Do Transformations | Learn how to graph an absolute value. |

Graphing Absolute Value Equations: Dilations and Reflections | Get practice graphing absolute values. |

### 1. What is a Matrix?

A matrix is an array of numbers enclosed in brackets that represents a system of equations. Explore matrices and the parts of a matrix and learn how to add, subtract, and multiply matrices.

### 2. How to Take a Determinant of a Matrix

The determinant is a simple but unique operation you can perform with a matrix. Learn how to solve for the determinant based on the size of the matrix, and study explanations of each type of matrix to expand your math vocabulary.

### 3. What is an Absolute Value?

Absolute value in mathematics involves focusing on the size of a number instead of its sign. Explore the distance from zero, notation of absolute values, and solving equations with absolute values.

### 4. How to Evaluate Absolute Value Expressions

An absolute value expression can be evaluated, but all operations contained within the absolute value bars must be completed before making it positive. Learn how to solve an absolute value expression by substituting individual variables and replacing groups of variables.

### 5. How to Solve an Absolute Value Equation

An absolute value equation includes a variable that is an absolute value as one of the variables resulting in two solutions, the positive or negative. Learn about the methods of solving basic absolute value equations and why it is necessary to split an absolute value equation into two possible equations to solve for the variable.

### 6. Solving Absolute Value Practice Problems

The solution to an absolute value problem will always include two answers that are arrived at by splitting the equation up. Learn how to solve for absolute value with a step-by-step introduction using an onion analogy.

### 7. How to Graph an Absolute Value and Do Transformations

Absolute value graphs are translations of standard graphs, created by using linear representations in the shape of a 'V' rather than the standard axis intersect. In this lesson, learn two of the most common transformations observed on absolute value graphs.

### 8. Graphing Absolute Value Equations: Dilations & Reflections

An absolute value is the numerical distance from zero and can be used in equations and graphed as dilations or reflections. Discover how translations apply to absolute value equations, and how dilations and reflections differ and are graphed.

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### Other Chapters

Other chapters within the Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Data, Statistics, and Probability