INTRODUCTION TO MATRIX ALGEBRA

Transforming Matrix Algebra for the STEM Undergraduate

 

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VECTORS

CHAPTER 02

 

PRE-REQUISITES & OBJECTIVES

 

Pre-Requisites for Vectors [PDF] [DOC]

Objectives of Vectors [PDF] [DOC]

TEXTBOOK CHAPTER
  Textbook Chapter on Vectors  [PDF] [DOC]
DIGITAL AUDIOVISUAL LECTURES
 

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]

MULTIPLE CHOICE TEST
  Test Your Knowledge of Vectors  [FLASH] [PDF] [DOC] [SOLUTION]
PROBLEM SET
  Problem set for Vectors [PDF]  [DOC]
PRESENTATIONS
 

PowerPoint Presentation of Vectors [PDF] [PPT]

RELATED TOPICS

 

Introduction

Vectors

Binary Operations

Unary Operations

System of Equations

Gaussian Elimination

Gauss-Seidel Method

LU Decomposition

Adequacy of Solutions

Eigenvalues and Eigenvectors

 

 


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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.