Math 260 Linear Algebra

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The following dates are TENTATIVE and are subject to change, including for exams.

Textbook Chapter 1     Syllabus (coming)    Exam Solutions     Octave    Octave online    Applications     IMT     Desmos matrix tool    Office hours (coming)    Do Good Sheet    $5 Challenge

Day Date Before class In class
supplements
Homework to turn in at the
beginning of our next class
HW
Sol.
Section Video clips (length) HO
Mon 1/13 Intro Don't be a slacker (do go the extra mile)  (7:38) Coins Activity
Tue 1/14 1.1 Row reduction  (7:36) 1.1 Nutrition Planning Example
Examples of row reduction
Gauss-Jordan Elimination Website
Another Gauss-Jordan Elimination Website
HW
1
Section 1.1, Page 10
2, 3, 8, 17, 18, 21 - 24,
26, 27, 30, 32

HW1
Thu 1/16 1.2 Infinite solutions   (17:42)
No solution   (12:07)
1.2 Some possible outcomes HW
2
Section 1.2, Page 21
1, 10 - 12, 15, 16, 19 - 23,
25 - 27, 30, 31

HW2
Fri 1/17 1.3 Vectors   (5:48)
Linear combinations, span (20:34)
1.3 Echelon forms: Span HW
3
Section 1.3, Page 32
6 - 13, 17, 20 - 27, 29,
31 (see 29), 32
Mon 1/20 No class MLK Day
Tue 1/21 1.4 Matrix equation Ax = b (through 7:00)   (7:00) 1.4 HW
4
Section 1.4, Page 40
1, 4, 9, 13, 15, 16,
21 - 25, 28, 30 - 32
Thu 1/23 1.5 Parametric vector form   (24:45) 1.5 HW
5
Section 1.5, Page 47
2, 3, 6, 14, 18, 23 - 25,
29 - 33, 35
Fri 1/24 1.6 Balancing chemical equations   (4:41)
Network flow   (8:18)
- HW
6
Section 1.6, Page 54
3, 7 - 9, 11, 13 - 15
Mon 1/27 1.7 Linear independence   (15:45) Echelon forms: Linear Ind. HW
7
Section 1.7, Page 60
2, 4, 11, 17 - 23,
25, 27, 34 - 39
Tue 1/28 1.8 Linear transformations   (13:52)
Image of a subset   (18:10)
The matrix arcade
Visualizing linear transformations
HW
8
Section 1.8, Page 68
2, 5, 8, 16, 18, 19, 21, 22,
29, 31, 33 - 35
Thu 1/30 1.9 The matrix of a linear transformation   (17:31)
Image of a linear transformation   (16:36)
Rotations, compositions, etc.   (10:03)
Rotations, reflections, etc. HW
9
Section 1.9, Page 78
1 - 3, 7, 16, 23 - 26,
28, 36
Fri 1/31 Review 1.R HW
10
Section 1.S, Page 88
1 (don't turn in), 5 - 8
10 - 12, 14 - 18, 21, 22
Mon 2/3 2.1 Matrix multiplication   (6:25) Excel matrix multiply, invert HW
11
Section 2.1, Page 100
2, 5, 7 - 9, 15, 16, 18, 20
21, 22, 24, 25
Tue 2/4 2.2 Matrix inverses   (14:14)
Use Matrix inverse to solve Ax = b   (6:39)
Excel matrix multiply, invert
Row reduction tool
Derivation of 2 x 2 inverse formula
3 x 3 inverse formula
HW
12
Section 2.2, Page 109
6, 7, 9, 10, 13, 16, 17,
19, 21, 22, 24, 35
Thu 2/6 2.3 HW
13
Section 2.3, Page 115
5, 11 - 18, 20 - 24, 27, 41a
Fri 2/7 2.4, 2.5 Block/partioned matrices   (17:36)
LU factorization   (8:22)
More on elementary matrices HW
14
Section 2.4, Page 121
6, 13, 25
Section 2.5, Page 129
2, 8, 9, 17
Mon 2/10 2.6 Input-output analysis   (6:04) Excel consumption matrix example HW
15
Section 2.6, Page 136
1 - 4, 7, 8, 10, 12
Tue 2/11 Review Section 2.S, Page 160
1 - 4, 6 - 10, 17, 19, 20
Thu 2/13 Exam 1
Fri 2/14 3.1 2 x 2 and 3 x 3 determinants   (10:00)
n x n determinants: part 1   (18:39)
n x n determinants: part 2   (9:02)
Shortcut for 3 x 3 determinants   (2:38)
Determinant, etc. finder
3 x 3 inverse formula
HW
16
Section 3.1, Page 167
2, 10, 16, 19, 20, 22, 26, 28
30, 34, 36, 38, 39, 40b, 41
Mon 2/17 3.2 Determinant after multiplying row   (13:19)
    (and correction)   (2:51)
Determinant after add row to another   (16:54)
Determinants after row operation   (10:24)
Determinant of triangular matrix   (8:06)
An example   (9:12)
Why det(AB)=det(A)*det(B) HW
17
Section 3.2, Page 175
2, 4, 16 - 20, 22, 24, 27,
28, 31 - 33, 36
Tue 2/18 3.3 Determinant & area of a parallelogram   (21:37)
Cramer's Rule   (11:07)
Visualizing Cramer's Rule HW
18
Section 3.3, Page 184
4, 6, 9, 10, 17, 18, 20, 22, 30
Thu 2/20 4.1 Vector spaces   (23:28) HW
19
Section 4.1, Page 195
2, 5, 6, 8, 16, 21, 23
24, 27, 28, 32, 33
Fri 2/21 4.2 Null space   (10:22)
Calculating null space   (13:06)
Column space   (10:39)
Visualizing column space   (21:10)
HW
20
Section 4.2, Page 205
2, 4, 7, 15, 23 - 26, 28
30, 39
Mon 2/24 4.3 Linear independence and null space   (9:31)
Bases for null space and column space   (25:12)
Pivot columns, basis for column space   (8:32)
HW
21
Section 4.3, Page 213
2, 3, 5, 6, 8, 14, 19, 21 - 24
29 - 32
Tue 2/25 4.4 Coordinates   (16:07) HW
22
Section 4.4, Page 222
4, 6, 13, 14, 18, 22,
23, 25, 27, 31
Thu 2/27 4.5 Nullity: dimension of nullspace   (13:58)
Rank: dimension of column space   (12:47)
HW
23
Section 4.5, Page 229
4, 8, 11, 14, 19 - 21,
25, 26, 29 - 31
Mon 2/28 4.6 HW
24
Section 4.6, Page 236
1, 2, 5 - 27
Mon 3/10 4.9 Origin of Markov Chains   (7:14)
Markov Chain matrix   (12:49)
Chutes and Ladders and Markov Chains HW
25
Section 4.9, Page 260
2, 3, 6, 7, 12, 13, 17,
18, 20, 21
Tue 3/11 5.1 Eigenvectors & e.values (through 2:16)   (2:16)
Visualizing eigenvectors in Excel
Eigenvalue/vector finder
Proof by induction video
HW
26
Section 5.1, Page 271
3, 4, 6, 10, 13, 16, 17,
21 - 25, 27, 30, 33
Thu 3/13 5.2 How to find eigenvalues  (4:35)   x is 0
Find eigenvalues example   (5:38)
HW
27
Section 5.2, Page 279
2, 8, 11, 16, 19, 21,
22, 25, 26
Fri 3/14 5.3 Matrix diagonalization   (11:36) HW 5.3.33 in Wolfram Alpha HW
28
Section 5.3, Page 286
2, 4, 5, 10, 11, 21 - 24
26 - 31
Mon 3/17 Review Review Example
Proof that stochastic matrix e-values ≤ 1
Section 5.S, Page 262
Don't turn in--for practice
1, 2, 3, 8, 9, 11 - 13
Tue 3/18 Exam 2
Thu 3/20 5.6 Predator-prey systems   (5:08)
Predator-prey spreadsheet
Fri 3/21 5.6 Predator-prey example   (10:16) Predator-prey spreadsheet HW
29
Section 5.6, Page 309
1, 2, 6 - 8, 10, 13
Mon 3/24 5.7 A Covid modelling example
Tue 3/25 5.7 HW
30
Section 5.7, Page 317
1, 2, 5 - 8
Thu 3/27 5.8 Power Method   (8:59) Power Method spreadsheet HW
31
Section 5.8, Page 321
1, 4 - 6, 8, 9, 19 - 21
Fri 3/28 6.1 Orthogonal complements   (6:00) Proof of The Law of Cosines HW
32
Section 6.1, Page 336
2, 3, 6, 7, 10, 14, 17,
19, 20, 22, 23, 25, 28, 30
Mon 3/31 6.2 Orthogonal sets  (11:55) HW
33
Section 6.2, Page 344
2, 3, 8, 9, 12, 14, 21,
23 - 25, 27 - 30
Tue 4/1 6.3 Orthogonal bases   (5:59) HW
34
Section 6.3, Page 352
1, 6, 8, 12, 13, 16, 19 - 24
Thu 4/3 6.4 Gram-Schmidt Process   (19:23) HW
35
Section 6.4, Page 358
3, 4, 7 - 10, 17 - 19
Fri 4/4 6.5 Least squares example (13:24) Calculus-based least sq. derivation
History of least squares
Ellipses and least squares
Summary of Least Squares
Summary of Techniques for Ax = b
    and   Eight Examples
HW
36
Section 6.5, Page 366
3, 4, 7, 8, 10, 11, 13,
17, 18, 22, 25
Mon 4/7 6.6 HW
37
Section 6.6, Page 374
2, 7 - 10, 13, 16
Tue 4/8 6.7 Inner Product Spaces   (12:08) Almost inner products HW
38
Section 6.7, Page 382
2, 3, 5, 7, 13, 15 - 26
Thu 4/10 Review
Fri 4/11 6.8 Intro to Fourier Series   (13:52) What are Fourier Series?   (8:24)
What are Fourier Series? Another view  (19:42)
HW
39
Section 6.8, Page 389
5 - 12
Mon 4/14 Exam 3
Tue 4/15 7.1 Column by row matrix multiplication   (12:02) HW
40
Section 7.1, Page 399
2, 4, 6, 8 - 10, 14, 17,
24 - 29, 31, 34, 35
Thu 4/17 IM Jacobi Method (6:50)
Gauss-Seidel Method (6:04)
IM1 Jacobi, Gauss-Seidel, SOR Spreadsheet
Fri 4/18 IM IM2
Mon 4/21 IM
Tue 4/22 Review
Mon 4/21 Review
Tue 4/22 Review
Thu 5/1 Final Exam 1:30 - 4:00 p.m.

HW Problems to work in class