INTRODUCTION TO MATRIX ALGEBRA

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VECTORS (CHAPTER 2)

 

How can vectors be used to write simultaneous linear equations?

 

By Autar Kaw

TOPIC DESCRIPTION
 

Learn how vectors can be used to write simultaneous linear equations.

 

This video teaches you how vectors can be used to write simultaneous linear equations.
ALL VIDEOS FOR THIS TOPIC
 

What is a vector? [YOUTUBE 2:27]  [TRANSCRIPT]

What is a vector? Example  [YOUTUBE 1:15] [TRANSCRIPT]

 

When are two vectors equal? [YOUTUBE 2:02][TRANSCRIPT]

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

 

How do you add two vectors? [YOUTUBE 1:34][TRANSCRIPT]

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

 

What is a null (or zero) vector? [YOUTUBE 1:12] [TRANSCRIPT]

What is a unit vector? [YOUTUBE 1:30][TRANSCRIPT]

 

What is a unit vector? Example [YOUTUBE 1:49] [TRANSCRIPT]
 

How do you multiply a vector by a scalar?  [YOUTUBE 1:18] [TRANSCRIPT]

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

 

What do you mean by linear combination of vectors? [YOUTUBE 1:44] [TRANSCRIPT]

What do you mean by linear combination of vectors? Example  [YOUTUBE 2:34][TRANSCRIPT]

What do you mean by vectors being linearly independent? [YOUTUBE 2:28] [TRANSCRIPT]
Are these vectors linearly independent? Example 1  [YOUTUBE 3:17] [TRANSCRIPT]

Are these vectors linearly independent? Example 2  [YOUTUBE 9:13][TRANSCRIPT]

 

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

Rank of a set of vectors: Example 2  [YOUTUBE 2:27] [TRANSCRIPT]

 

Prove that if a set of vectors contains a null vector, the set of vectors is linearly dependent  [YOUTUBE 2:29] [TRANSCRIPT]

Prove that if a set of vectors is linearly independent, then a subset of it is also linearly independent  [YOUTUBE 5:42][TRANSCRIPT]

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] [TRANSCRIPT]
 

How can vectors be used to write simultaneous linear equations?  [YOUTUBE 5:08] [TRANSCRIPT]

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

 

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

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.

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved.

Questions, suggestions or comments, contact kaw@usf.edu 

This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions orCreative Commons License recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Based on a work at http://mathforcollege.com/ma.  Introduction to Matrix Algebra is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.