Math 260 Linear Algebra

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

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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   HW  
Mon 1/8 Intro Don't be a slacker (do go the extra mile)  (7:38) Coins Activity
Tue 1/9 1.1 Row reduction  (7:36) 1.1 1.1
2, 8 		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 1/11 1.2 Infinite solutions   (17:42)
No solution   (12:07) 		1.2 1.2
10, 16 		Some possible outcomes HW
2		 Section 1.2, Page 21
1, 10 - 12, 15, 16, 19 - 23,
25 - 27, 30, 31 		HW2
Fri 1/12 1.3 Vectors   (5:48)
Linear combinations, span (20:34) 		1.3 1.3
6, 12		 Echelon forms: Span HW
3		 Section 1.3, Page 32
6 - 13, 17, 20 - 27, 29,
31 (see 29), 32 		HW3
Mon 1/15 No class
Tue 1/16 1.4 Matrix equation Ax = b (through 7:00)   (7:00) 1.4 1.4
4, 22		 HW
4		 Section 1.4, Page 40
1, 4, 9, 13, 15, 16,
21 - 25, 28, 30 - 32 		HW4
Thu 1/18 1.5 Parametric vector form   (24:45) 1.5 None HW
5		 Section 1.5, Page 47
2, 3, 6, 14, 18, 23 - 25,
29 - 33, 35 		HW5
Fri 1/19 1.6 Balancing chemical equations   (4:41)
Network flow   (8:18) 		- None HW
6		 Section 1.6, Page 54
3, 7 - 9, 11, 13 - 15		 HW6
Mon 1/22 1.7 Linear independence   (15:45) 1.7 1.7
16 - 19 		Echelon forms: Linear Ind. HW
7		 Section 1.7, Page 60
2, 4, 11, 17 - 23,
25, 27, 34 - 39 		HW7
Tue 1/23 1.8 Linear transformations   (13:52)
Image of a subset   (18:10)
 1.8 1.8
2, 8 		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 		HW8
Thu 1/25 1.9 The matrix of a linear transformation   (17:31)
Image of a linear transformation   (16:36)
Rotations, compositions, etc.   (10:03) 		1.9 1.9
6, 18 		Rotations, reflections, etc. HW
9		 Section 1.9, Page 78
1 - 3, 7, 16, 23 - 26,
28, 36 		HW9
Fri 1/26 Review 1.R None HW
10		 Section 1.S, Page 88
1 (don't turn in), 5 - 8
10 - 12, 14 - 18, 21, 22 		HW10
Mon 1/29 2.1 Matrix multiplication   (6:25) 2.1 2.1
5, 8 		Excel matrix multiply, invert HW
11		 Section 2.1, Page 100
2, 5, 7 - 9, 15, 16, 18, 20
21, 22, 24, 25		 HW11
Tue 1/30 2.2 Matrix inverses   (14:14)
Use Matrix inverse to solve Ax = b   (6:39) 		2.2 2.2
10 		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 		HW12
Thu 2/1 2.3 2.3 2.3
12 		HW
13		 Section 2.3, Page 115
5, 11 - 18, 20 - 24, 27, 41a 		HW13
Fri 2/2 2.4, 2.5 Block/partioned matrices   (17:36)
LU factorization   (8:22) 		2.4
2.5 		None More on elementary matrices HW
14		 Section 2.4, Page 121
6, 13, 25
Section 2.5, Page 129
2, 8, 9, 17 		HW14
Mon 2/5 No class
Tue 2/6 2.6 Input-output analysis   (6:04) 2.6 None Excel consumption matrix example HW
15		 Section 2.6, Page 136
1 - 4, 7, 8, 10, 12 		HW15
Thu 2/8 Review Section 2.S, Page 160
Don't turn in--for practice
1 - 4, 6 - 10, 17, 19, 20
Fri 2/9 Exam 1
Mon 2/12 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) 		3.1 3.1
26, 30		 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 		HW16
Tues 2/13 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) 		3.2 3.2
6 		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		 HW17
Thu 2/15 3.3 Determinant & area of a parallelogram   (21:37)
Cramer's Rule   (11:07) 		3.3 3.3
4 		Visualizing Cramer's Rule HW
18		 Section 3.3, Page 184
4, 6, 9, 10, 17, 18, 20, 22, 30 		HW18
Fri 2/16 No class
Mon 2/19 4.1 Vector spaces   (23:28) 4.1 None HW
19		 Section 4.1, Page 195
2, 5, 6, 8, 16, 21, 23
24, 27, 28, 32, 33		 HW19
Tue 2/20 4.2 Null space   (10:22)
Calculating null space   (13:06)
Column space   (10:39)
Visualizing column space   (21:10) 		4.2 4.2
24 		HW
20		 Section 4.2, Page 205
2, 4, 7, 15, 23 - 26, 28
30, 39		 HW20
Thu 2/22 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) 		4.3 4.3
8 		HW
21		 Section 4.3, Page 213
2, 3, 5, 6, 8, 14, 19, 21 - 24
29 - 32 		HW21
Fri 2/23 4.4 Coordinates   (16:07) 4.4 4.4
4, 6 		HW
22		 Section 4.4, Page 222
4, 6, 13, 14, 18, 22,
23, 25, 27, 31 		HW22
Mon 3/4 4.5 Nullity: dimension of nullspace   (13:58)
Rank: dimension of column space   (12:47) 		4.5 4.5
8 		HW
23		 Section 4.5, Page 229
4, 8, 11, 14, 19 - 21,
25, 26, 29 - 31 		HW23
Tue 3/5 4.6 4.6 4.6
2 		HW
24		 Section 4.6, Page 236
1, 2, 5 - 27 		HW24
Thu 3/7 4.9 Origin of Markov Chains   (7:14)
Markov Chain matrix   (12:49) 		4.9 4.9
6 		HW
25		 Section 4.9, Page 260
2, 3, 6, 7, 12, 13, 17,
18, 20, 21 		HW25
Fri 3/8 5.1 Eigenvectors & e.values (through 2:16)   (2:16)
 5.1 5.1
4 		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 		HW26
Mon 3/11 5.2 How to find eigenvalues  (4:35)   x→ is ≠ 0
Find eigenvalues example   (5:38) 		5.2 5.2
2 		HW
27		 Section 5.2, Page 279
2, 8, 11, 16, 19, 21,
22, 25, 26 		HW27
Tue 3/12 5.3 Matrix diagonalization   (11:36) 5.3 5.3
2 		HW 5.3.33 in Wolfram Alpha HW
28		 Section 5.3, Page 286
2, 4, 5, 10, 11, 21 - 24
26 - 31 		HW28
Thu 3/14 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 		5.SE
Fri 3/15 Exam 2
Mon 3/18 5.6 Predator-prey systems   (5:08)
5.6 Predator-prey spreadsheet
Tue 3/19 5.6 Predator-prey example   (10:16) Predator-prey spreadsheet HW
29		 Section 5.6, Page 309
1, 2, 6 - 8, 10, 13 		HW29
Thu 3/21 5.7 5.7 A Covid modelling example
Fri 3/22 5.7 HW
30		 Section 5.7, Page 317
1, 2, 5 - 8 		HW30
Mon 3/25 5.8 Power Method   (8:59) 5.8 Power Method spreadsheet HW
31		 Section 5.8, Page 321
1, 4 - 6, 8, 9, 19 - 21 		HW31
Tue 3/26 6.1 Orthogonal complements   (6:00) 6.1 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 		HW32
Thu 3/28 6.2 Orthogonal sets  (11:55) 6.2 HW
33		 Section 6.2, Page 344
2, 3, 8, 9, 12, 14, 21,
23 - 25, 27 - 30 		HW33
Fri 3/29 6.3 Orthogonal bases   (5:59) 6.3 HW
34		 Section 6.3, Page 352
1, 6, 8, 12, 13, 16, 19 - 24 		HW34
Mon 4/1 6.4 Gram-Schmidt Process   (19:23) 6.4 HW
35		 Section 6.4, Page 358
3, 4, 7 - 10, 17 - 19 		HW35
Tue 4/2 6.5 Least squares example (13:24) 6.5
and
6.6 		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 		HW36
Thu 4/4 6.6 HW
37		 Section 6.6, Page 374
2, 7 - 10, 13, 16 		HW37
Fri 4/5 6.7 Inner Product Spaces   (12:08) 6.7 Almost inner products HW
38		 Section 6.7, Page 382
2, 3, 5, 7, 13, 15 - 26 		HW38
Mon 4/8 Review
Tue 4/9 6.8 Intro to Fourier Series   (13:52) 6.8 What are Fourier Series?   (8:24)
What are Fourier Series? Another view  (19:42) 		HW
39		 Section 6.8, Page 389
5 - 12 (due Monday, 4/15)
Thu 4/11 Exam 3
Fri 4/12 7.1 Column by row matrix multiplication   (12:02) 7.1 HW
40		 Section 7.1, Page 399
2, 4, 6, 8 - 10, 14, 17,
24 - 29, 31, 34, 35
Mon 4/15 IM Jacobi Method (6:50)
Gauss-Seidel Method (6:04) 		IM1 Jacobi, Gauss-Seidel, SOR Spreadsheet
Tue 4/16 IM IM2
Thu 4/18 IM
Fri 4/19 No class
Mon 4/22 Take-home Final Exam due to my office RAC 115 by 1:30 pm