Chapter 02 Rank of a Set of Vectors Example 2 – Introduction to Matrix Algebra

Vectors (CHAPTER 2)

Topic

Rank of a set of vectors: Example 2

Summary

Learn about the rank of a set of vectors through another example.

Learning Objective

This video teaches you about the rank of a set of vectors through another example.

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.