Ch 3: Vectors in Linear Algebra Lesson Plans

About This Chapter

The Vectors in Linear Algebra Lesson Plans chapter of this course is designed to help you plan and teach linear algebra in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Vectors in Linear Algebra 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 Vectors Scalars, vectors, math operations on vectors, and dot products
Tuesday Vector Spaces Definition of and operations using vector spaces/subspaces and vector space basis
Wednesday Orthonormal bases Working with orthonormal bases and vectors, including the Gram-Schmidt process
Thursday Linear combinations How to use linear combinations and linear span to solve for vectors
Friday Linear independence Define linear dependence/independence and provide applications of their use

9 Lessons in Chapter 3: Vectors in Linear Algebra Lesson Plans
Test your knowledge with a 30-question chapter practice test
Scalars and Vectors: Definition and Difference

1. Scalars and Vectors: Definition and Difference

In this lesson, we will examine scalars and vectors, learn why it is important to know the difference between the two and why remembering to add a direction to many of your exam answers could be the reason you get it right or wrong.

Performing Operations on Vectors in the Plane

2. 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.

The Dot Product of Vectors: Definition & Application

3. 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.

Vector Spaces: Definition & Example

4. Vector Spaces: Definition & Example

In this lesson, we'll discuss the definition and provide some common examples of vector spaces. We'll go over set theory, the axioms for vector spaces, and examples of axioms using vector spaces of the real numbers over a field of real numbers.

Finding the Basis of a Vector Space

5. Finding the Basis of a Vector Space

In this lesson we'll start by reviewing matrix reduced row echelon form, which is integral to finding a basis of a vector space. Then we'll work through a problem together to see exactly how finding a basis is accomplished.

Orthonormal Bases: Definition & Example

6. Orthonormal Bases: Definition & Example

In this lesson we show how independent vectors in a space can become a basis for the space and how this basis can be turned into an orthonormal basis. Having an orthonormal basis is useful in many applications involving vectors.

The Gram-Schmidt Process for Orthonormalizing Vectors

7. The Gram-Schmidt Process for Orthonormalizing Vectors

Linearly combining things is something we do quite naturally. When the things are vectors, there is a fantastic way to organize the vectors before combining them. In this lesson, we'll show how to orthonormalize vectors using the Gram-Schmidt process.

Linear Combinations & Span: Definition & Equation

8. Linear Combinations & Span: Definition & Equation

This lesson will cover the definitions of linear combinations and spans in terms of vector spaces, using a real world example and then a mathematical example. You will learn the official definitions and how to apply them in mathematics.

Linear Dependence & Independence: Definition & Examples

9. Linear Dependence & Independence: Definition & Examples

Linear dependence and independence are based on whether or not there is more than one solution to a system of equations. In this lesson, we'll look at how you can determine whether or not a system is independent and work through some examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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