About This Chapter
Below is a sample breakdown of the Vectors, Matrices and Determinants chapter into two school weeks (10 school days). 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|| Performing operations on vectors|
Dot product of vectors
| Perform addition, subtraction and multiplication on vectors in a plane. Solve applied problems using vectors|
Definition, identification and application of the dot product of vectors
|Tuesday|| The matrix|
| Definition of a matrix|
Definition of an augmented matrix and how to write one for a linear system
|Wednesday||Matrix row operations|
Solving systems using inverse matrices
| Definition of matrix row operations and how to perform them|
Definition of equal matrices and matrix notation. Explanation of how to add, subtract and multiply matrices
Identify and solve inverse matrices
|Thursday||Solving linear systems using Gaussian elimination||Definition of Gaussian elimination and how it can be used to solve linear systems|
|Friday|| Solving linear systems using Gauss-Jordan elimination|
Inconsistent and dependent systems
| Definition of Gauss-Jordan elimination and how it can be used to solve linear systems|
Application of Gaussian elimination to systems without unique solutions or systems with more variables than equations
|Monday||Multiplicative inverses of matrices and matrix equations||Finding the multiplicative inverse of a square matrix and how to use it to solve matrix equations.|
|Tuesday||Determinant of a matrix||Definition and steps to take a determinant of a matrix|
|Wednesday||Systems of linear equations in two and three-variables||Evaluation of second and third-order determinants. Use of Cramer's rule to solve a system of linear equations with two or three variables|
|Thursday||Cramer's rule with inconsistent and dependent systems||How to use determinants to identify inconsistent and dependent systems|
|Friday||How to evaluate higher-order determinants||Evaluation of higher-order determinants|
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 Trigonometry Curriculum Resource & Lesson Plans course
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