Chapter 02 What do you Mean by Vectors Being Linearly Independent

Vectors (CHAPTER 2)

Topic

What do you mean by vectors being linearly independent?

Summary

Learn what it means by vectors being linearly independent.

Learning Objective

This video teaches you what it means when vectors are linearly independent.

Transcript

Read the transcript

All Videos for this Topic

- - What is a vector? [YOUTUBE 2:27]
  - What is a vector? Example [YOUTUBE 1:15]

- - When are two vectors equal? [YOUTUBE 2:02]
  - When are two vectors equal? Example [YOUTUBE 2:26]

- - How do you add two vectors? [YOUTUBE 1:34]
  - How do you add two vectors? Example [YOUTUBE 1:48]

- - What is a null (or zero) vector? [YOUTUBE 1:12]
  - What is a unit vector? [YOUTUBE 1:30]
  - What is a unit vector? Example [YOUTUBE 1:49]

- - How do you multiply a vector by a scalar? [YOUTUBE 1:18]
  - How do you multiply a vector by a scalar? Example [YOUTUBE 1:16]

- - What do you mean by linear combination of vectors? [YOUTUBE 1:44]
  - What do you mean by linear combination of vectors? Example [YOUTUBE 2:34]
  - What do you mean by vectors being linearly independent? [YOUTUBE 2:28]
  - Are these vectors linearly independent? Example 1 [YOUTUBE 3:17]
  - Are these vectors linearly independent? Example 2 [YOUTUBE 9:13]

- - What do you mean by rank of a set of vectors? [YOUTUBE 2:09]
  - Rank of a set of vectors: Example 1 [YOUTUBE 3:53]
  - Rank of a set of vectors: Example 2 [YOUTUBE 2:27]

- - Prove that if a set of vectors contains a null vector, the set of vectors is linearly dependent [YOUTUBE 2:29]
  - Prove that if a set of vectors is linearly independent, then a subset of it is also linearly independent [YOUTUBE 5:42]
  - Prove that if a set of vectors is linearly dependent, then at least one vector can be written as a linear combination of others [YOUTUBE 4:06]

- - How can vectors be used to write simultaneous linear equations? [YOUTUBE 5:08]
  - How can vectors be used to write simultaneous linear equations? Example [YOUTUBE 3:13]

- - What is the definition of the dot product of two vectors? [YOUTUBE 2:00]
  - Dot product of two vectors Example [YOUTUBE 1:41]

Complete Resources

Get in one place the following: a textbook chapter, a PowerPoint presentation, individual YouTube lecture videos, multiple-choice questions, and problem sets on Vectors.