# Ch 11: Honors Algebra 1: Matrices in Linear Equations

### About This Chapter

Honors Algebra 1: Matrices in Linear Equations - Chapter Summary and Learning Objectives

This chapter will explain the importance of matrices in linear equations in algebra. You can assess how problems involving these matrices are solved. These engaging video lessons will help you focus on learning more about:

- The definition of a matrix
- Augmented matrices, matrix notation, equal matrices and operations with matrices
- Matrix row operations and inverse matrices
- Gaussian elimination
- Cramer's Rule
- The determinant of a matrix

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

What is a Matrix? | Evaluate matrices and why they are useful. |

How to Write an Augmented Matrix for a Linear System | Calculate how to shift a system of equations into an augmented matrix. |

Matrix Notation, Equal Matrices & Math Operations with Matrices | Consider the basics about matrices and learn how they're used in mathematics. |

How to Perform Matrix Row Operations | Learn how to solve problems that involve matrix row operations. |

How to Solve Inverse Matrices | Evaluate inverse matrices and determine why they are useful. |

How to Solve Linear Systems Using Gaussian Elimination | Focus on how to use Gaussian elimination to manipulate a matrix. |

Inconsistent and Dependent Systems: Using Gaussian Elimination | Survey methods for handling inconsistent and dependent systems. |

Using Cramer's Rule with Inconsistent and Dependent Systems | Assess what happens when Cramer's Rule is applied to inconsistent and dependent systems. |

How to Take a Determinant of a Matrix | Devise the method for taking a determinant of a matrix. |

### 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. 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.

### 4. 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.

### 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. 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.

### 8. 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.

### 9. 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!

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### Other Chapters

Other chapters within the Honors Algebra 1 Textbook course

- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math