About This Chapter
Who's it for?
This unit of our High School Precalculus Homeschool course will benefit any student who is trying to learn how to solve vectors and matrices. There is no faster or easier way to learn about mathematics. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn how to evaluate higher-order determinants and use Cramer's rule with dependent systems.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a mathematics curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Vectors and Matrices unit exam confirm understanding or identify any topics that require review.
Vectors and Matrices Unit Objectives:
- Give the definition of a matrix.
- Discover how to perform matrix row operations.
- Solve a system of equations in three variables.
- Solve inverse matrices.
- Calculate the multiplicative inverse of a square matrix.
- Write an augmented matrix for a linear system.
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. 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.
5. 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!
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
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 within the High School Precalculus: Homeschool Curriculum course
- Graphing Linear Equations: Homeschool Curriculum
- Solving & Graphing Inequalities: Homeschool Curriculum
- Absolute Value Expressions: Homeschool Curriculum
- Graphing Complex Numbers: Homeschool Curriculum
- Solving Linear Systems: Homeschool Curriculum
- Linear Models: Homeschool Curriculum
- Quadratics: Homeschool Curriculum
- Quadratic Functions & Equations: Homeschool Curriculum
- Geometry Basics: Homeschool Curriculum
- Functions for Precalculus: Homeschool Curriculum
- Using Function Operations: Homeschool Curriculum
- Recognizing Graph Symmetry: Homeschool Curriculum
- How to Graph Functions: Homeschool Curriculum
- Rate of Change: Homeschool Curriculum
- Polynomial Functions: Homeschool Curriculum
- Higher-Degree Polynomials: Homeschool Curriculum
- Difference Quotients in Precalculus: Homeschool Curriculum
- Working with Rational Expressions: Homeschool Curriculum
- Evaluating Logarithmic Functions: Homeschool Curriculum
- Functions in Trigonometry: Homeschool Curriculum
- Using Trigonometric Graphs: Homeschool Curriculum
- Trigonometric Equations: Homeschool Curriculum
- Basic Trigonometric Identities: Homeschool Curriculum
- Laws of Sine & Cosine: Homeschool Curriculum
- Graphing Piecewise Functions: Homeschool Curriculum
- Mathematical Sequences: Homeschool Curriculum
- Identifying Conic Sections: Homeschool Curriculum
- Parametric Equations: Homeschool Curriculum
- Continuity: Homeschool Curriculum
- Limits in Precalculus: Homeschool Curriculum
- Groups & Sets in Algebra: Homeschool Curriculum