MA-305 Transparencies for Lecture 14
Thursday, February 26, 1998
Slide 1
Defining a Vector Space - (Audio Part 1, 3:08)
Defining a Field - (Audio Part 1, 8:23)
Vector Space Example - (Audio Part 1, 9:27)
Slide 2
Verifying that our Example is a Vector Space
(Identity, Commutivity, and Negation Properties)
(Audio Part 1, 12:32)
Slide 3
Another Vector Space Example
(Audio Part 1, 17:38)
Slide 4
More Vector Space Examples Examined:
Rn - Vector Addition and Multiplication
(Audio Part 1, 23:52)
Slide 5
Proving Property of Multiplication by 0-scalar
(Audio Part 1, 30:20)
Multiplying by 1-scalar
(Audio Part 1, 35:01)
Slide 6
Considering Vector Addition
(Audio Part 1, 37:48)
Slide 7
Vectors in 3-space and Homogeneous Linear Systems
(Audio Part 1, 45:00)
Solutions as a Vector (sub-)Space
(Audio Part 1, 52:52)
Slide 8
Is a Line Through the Origin a Vector Space?
(Audio Part 1, 53:37)
Checking Closure Under Scalar Multipliation
and Vector Addition
(Audio Part 2, 0:01)
Slide 9
Verifying Closure Under Scalar Multiplicatino
(Audio Part 2, 2:00)
Theorem for Subsets of a Vector Space as
as a Vector Space
(Audio Part 2, 5:31)
Slide 10
Defining a Subspace
(Audio Part 2, 7:40)