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VECTORS (CHAPTER 2)

What is a vector?: Example

By Autar Kaw

TOPIC DESCRIPTION

Learn what the definition of a vector is through an example.

This video teaches you what a vector is through an example.

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]

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, , 0836805, 1322586.  Any opinions, findings, and conclusions or 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.