# Introduction to Linear Algebra: Vectors

## Introduction to Linear Algebra: Vectors

### Learn the basic arithmetic operations on vectors

#### What youâ€™ll learn

Introduction to Linear Algebra: Vectors

• Add and scale vectors specified geometrically or component-wise
• Write the definition of a linear combination of two vectors
• Write a vector as a linear combination of other vectors
• Identify in simple cases if a vector is in the span of others
• Write the definition of the dot product of two vectors written in components as well as the geometric definition of the dot product involving lengths and angles
• Compute dot products and lengths
• Find the angle between two vectors
• Define and produce unit vectors
• Define orthogonality
• Demonstrate understanding of and apply Cauchy-Schwarz Inequality and Triangle Inequality

#### Requirements

• Familiar with precalculus (algebra, trigonometry, and functions)

#### Description

HOW DOES THIS COURSE WORK:

This course, Introduction to Linear Algebra: Vectors, includes the first section you will learn in Linear Algebra, including a video, notes from the whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:

• Geometric Vectors
• Algebraic Vectors
• Linear Combination
• The span of a Set of Vectors
• The Norm
• The Dot Product
• Cauchy-Schwarz Inequality
• Triangle Inequality

#### CONTENT YOU WILL GET INSIDE EACH SECTION:

Videos

: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issues you may encounter in class and make sure you can solve any problem by yourself.

Notes

: In each section, you will find my notes as a downloadable resource that I wrote during lectures. So you can review the notes even when you donâ€™t have internet access (but I encourage you to take your notes while taking the course!).

Assignments

: After you watch me doing some examples, now itâ€™s your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.

#### THINGS THAT ARE INCLUDED IN THE COURSE:

HIGHLIGHTS:

#1:

Downloadable lectures so you can watch the videos whenever and wherever you are.

#2:

Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

#3:

One problem set at the end of the course (with solutions!) for you to do more practice.

#4:

See you inside the course!

â€“ Gina ðŸ™‚

#### Who this course is for:

• Anyone who has completed precalculus (algebra and trigonometry) and wants to learn some more advanced math
• Current Linear Algebra students who are looking for extra help on vectors
• Anyone who is not in the science stream but wants to study Linear Algebra for fun