# Ch 26: Vectors, Matrices & Determinants: Lesson Plans

### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Vectors, Matrices and Determinants chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | The Dot Product of Vectors: Definition and Application; What is a Matrix?; How to Write an Augmented Matrix for a Linear System; How to Perform Matrix Row Operations | Calculating the algebraic and geometric dot product of vectors; The different components of a matrix; The techniques for writing an augmented matrix; Adding, multiplying and switching in a matrix |

Tuesday | Matrix Notation, Equal Matrices and Math Operations with Matrices; How to Solve Inverse Matrices; How to Solve Linear Systems Using Gaussian Elimination | The process of properly labeling matrices; The differences between identity and inverse matrices; Transforming linear systems into augmented matrices |

Wednesday | How to Solve Linear Systems Using Gauss-Jordan Elimination; Inconsistent and Dependent Systems: Using Gaussian Elimination; Multiplicative Inverses of Matrices and Matrix Equations | An explanation of this process; The differences between these systems; Techniques for solving matrices |

Thursday | How to Take a Determinant of a Matrix; Solving Systems of Linear Equations in Two Variables Using Determinants; Solving Systems of Linear Equations in Three Variables Using Determinants | Examples of square matrices; The steps for using Cramer's rule to solve linear systems; Techniques for finding determinants and solving a system of equations |

Friday | Using Cramer's Rule with Inconsistent and Dependent Systems; How to Evaluate Higher-Order Determinants in Algebra | Identifying inconsistent and dependent systems; A description of higher-order and minor matrices |

### 1. Performing Operations on Vectors in the Plane

After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.

### 2. The Dot Product of Vectors: Definition & Application

After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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!

### 13. 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.

### 14. 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.

### 15. 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.

### 16. 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

Other chapters within the High School Precalculus Syllabus Resource & Lesson Plans course

- Linear Equations: Precalculus Lesson Plans
- Inequalities: Precalculus Lesson Plans
- Absolute Value Equations: Precalculus Lesson Plans
- Complex Numbers: Precalculus Lesson Plans
- Systems of Linear Equations: Precalculus Lesson Plans
- Mathematical Modeling: Precalculus Lesson Plans
- Solving Quadratics: Precalculus Lesson Plans
- Quadratic Functions: Precalculus Lesson Plans
- Geometry Basics for Precalculus Lesson Plans
- Functions: Precalculus Lesson Plans
- Function Operations: Precalculus Lesson Plans
- Graph Symmetry: Precalculus Lesson Plans
- Graphing with Functions: Precalculus Lesson Plans
- Rate of Change: Precalculus Lesson Plans
- Polynomial Functions: Precalculus Lesson Plans
- Advanced Polynomial Functions: Precalculus Lesson Plans
- Rational Functions & Difference Quotients: Lesson Plans
- Rational Expressions & Function Graphs: Lesson Plans
- Exponential & Logarithmic Functions: Lesson Plans
- Trigonometric Functions: Precalculus Lesson Plans
- Trigonometric Graphs: Precalculus Lesson Plans
- Solving Trigonometric Equations: Lesson Plans
- Trigonometric Identities: Precalculus Lesson Plans
- Trigonometric Applications: Precalculus Lesson Plans
- Graphing Piecewise Functions: Precalculus Lesson Plans
- Mathematical Sequences & Series: Lesson Plans
- Sets in Algebra: Precalculus Lesson Plans
- Analytic Geometry & Conic Sections: Lesson Plans
- Polar Coordinates & Parameterizations: Lesson Plans
- Continuity: Precalculus Lesson Plans
- Limits: Precalculus Lesson Plans