Linear Algebra - MAT223 Instructor Guide

✍ Scribed by Jason Siefken

• Tongue: English
• Leaves: 108
• Edition: 2021/08/06
• Category: Library

✦ Table of Contents

Lessons
Lesson 1 – Linear Combinations
The Magic Carpet Ride
1
Lesson 2 – Linear Combinations
The Magic Carpet Ride, Hide and Seek
2
3
4
5
Lesson 3 – Visualizing Sets, Formal Language of Linear Combinations
6
7
8
Lesson 4 – Restricted Linear Combinations, Lines
9
10
Lesson 5 – Vector Form of Lines, Intersecting Lines
11
12
Lesson 6 – Planes, Span
13
14
15
Lesson 7 – Span, Translated Span
16
17
Lesson 8 – Linear Independence & Dependence
The Magic Carpet Ride, Getting Back Home
18
19
20
Lesson 9 – Linear Independence & Dependence—Equivalent Definitions
21
22
Linear Independence and Dependence, Creating Examples
23
Lesson 10 – Dot Product, Orthogonality
24
25
26
Lesson 11 – Normal Form of Lines and Planes
27
28
29
Lesson 12 – Projections
30
31
32
Lesson 13 – Projections, Subspaces
33
34
Lesson 14 – Basis, Dimension
35
36
Lesson 15 – Matrices
37
38
39
40
Lesson 16 – Change of Basis I
41
42
Lesson 17 – Orientation, Matrix Transformations
43
Italicizing N
44
Lesson 18 – Linear Transformations I
Beyond the N
45
46
47
Lesson 19 – Linear Transformations II, Composition of Linear Transformations
48
Pat and Jamie
49
Lesson 20 – Composition & Matrix Transformations, Range, Nullspace
50
51
52
Lesson 21 – Fundamental Subspaces
53
54
55
56
Lesson 22 – Rank
57
58
59
60
Lesson 23 – Rank-nullity Theorem, Inverses I
61
62
Getting back N
63
Lesson 24 – Inverses II, Elementary Matrices
64
65
66
Lesson 25 – Applications of Inverses I
67
68
69
Lesson 26 – Applications of Inverses II, Change of Basis
70
71
Lesson 27 – Determinants
72
73
74
75
76
Lesson 28 – Determinants and Compositions
77
78
79
80
81
Lesson 29 – Eigenstuff I
The Green and the Black
82
Lesson 30 – Eigenstuff II
83
84
85
Lesson 31 – Characteristic Polynomial, Diagonalization I
86
87
88
Lesson 32 – Diagonalization II
89
90
Lesson 33 – Diagonalization III
91