Math 324 Linear Algebra II
Monday, Wednesday, and Friday 9:10-10:00am
Hayes Hall 203
Textbook
Linear Algebra, A Modern Introduction, Third Edition, by David Poole.
Office Hours (Hayes 309-A)
Monday 2:10-3:00pm
Tuesday
11:10am-1:00pm
Wednesday
2:10-3:00pm
Thursday
10:10-11:00am
Homework
|
Lesson |
Date |
Section(s) |
Topic |
Homework |
Due |
|
1 |
1/14/2013 |
6.1 |
Vector Spaces
and Subspaces |
Worksheet: #3 #10: Give a rigorous argument that each of the 10
properties holds for the vector space. Read Syllabus
and Section 6.1. |
1/16/2013 |
|
2 |
1/16/2013 |
6.1 |
Vector Spaces
and Subspaces |
Worksheet: #6, 7, 9d In questions 6 and 7, just give a yes/no answer for (a).
Also for 6 and 7, provide a spanning set for Section 6.1: #4, 17, 18 (just show that axioms 1 and 6 hold), 22, 23, 38, 53, 55-57, 63, 64 |
1/23/2013 |
|
|
1/18/2013 1/21/2013 |
6.2 6.2 |
Linear Independence,
Basis, and Dimension |
Section 6.2: #3, 7, 13, 21, 22, 23, 27, 28, 34, 36,
39, 48, 49 Section 6.2 Worksheet (not Wronskian worksheet): #5 Think about #6, 7 for Wednesday. Read Section 6.2. |
|
|
3 |
1/23/2013 |
6.3 |
Change of
Basis |
Section 6.3: #2, 6, 10, 13, 16, 20, 21 Section 6.2: #33 (write up both halves) The Shape of the Future, Back to the Future Worksheets Read Section 6.3, 6.4, and 6.5. |
1/30/2013 |
|
4 |
1/30/2013, 2/1/2013, 2/4/2013, 2/6/2013 |
6.4-6.5 |
Linear
Transformations, Kernel, Range, Isomorphism |
Sec
6.4: #5, 16, 20, 24, 30, 34, Sec 6.5: #4, 8, 14, 21, 26, 32, 33,
37 Read Section 6.6, prepare
presentations. |
2/6/2013 |
|
5 |
2/8/2013,
2/11/2013 |
6.6 |
The Matrix of
a Linear Transformation |
Worksheet Sec
6.6: #15, 29, 39, 45, 46 Challenge
Problems (read as
“fun but not required”): 40, 41 |
2/13/2013 |
|
6 |
2/13/2013,
2/15/2013 |
Chapter 6 |
Review |
Review
worksheet (to be graded for completion) Read
Section 7.1. |
2/20/2013 |
|
7 |
2/20/2013,
2/22/2013 |
7.1 |
Inner Product
Spaces |
Sec
7.1: #2, 4, 9-11, 13, 16, 18, 20, 21, 27, 32 7.0
Taxicab: #6-8 Worksheet
on Read
Section 7.2. Challenge Problem: Prove that projW(v) and perpW(v) are orthogonal. |
2/27/2013 |
|
8 |
2/25/2013,
2/27/2013, 3/1/2013, 3/18/2013 |
7.2 |
Norms and
Distance Functions |
Sec
7.2: #2-4, 7-9, 14, 15, 24, 30, 32, 33, 40, 43, 45, 46, 48 Read
Sections 7.3 and 7.4. |
3/20/2013 |
|
9 |
3/22/2013, 3/25/2013 |
7.3 |
Least Squares
Approximation |
HW
from Jacobi proof: Sec
7.3: #10, 16, 24, 26, 29, 34, 28, 38,
44, 50, 53-55 |
3/27/2013 |
|
10 |
3/25/2013,
3/27/2013 |
7.4 |
The Singular
Value Decomposition! :) |
Section
7.4: #11, 15, 18, 19, 21, 24-30,
34, 35 #65:
For the matrix A in question 10, confirm that each part of Theorem 7.15
holds. Challenge
Problems: (1) Prove
Thm 7.15(a) by proving Section 3.5 #61. (2)
Prove Thm 5.25 and explain its connection to the svd. You may use a computer algebra system to help with
computations for this assignment (such as computing eigenvectors of ATA),
but you should make a note to that effect and write what the output at each
step is. |
4/3/2013 |
|
11 |
3/29/2013,
4/1/2013, 4/3/2013, 4/5/2013 |
7.4, Matlab |
The Singular
Value Decomposition |
In-class
worksheet MatLab
Problems (Choose 2 from the list of 5) Email Professor Smith with questions if you haven’t done so
yet! |
4/10/2013 |
|
12 |
4/8/2013,
4/10/2013, 4/12/2013 |
7.4 |
The Singular
Value Decomposition |
Section
7.4: #39, 40, 43, 47, 51 |
4/17/2013 |
|
13 |
4/17/2013 |
Chapter 7 |
Review |
Review assignment – not to be collected. Chapter
Review, pg. 646-647: 1
(b)-(d), (h)-(j), 2-6, 7 or 8, 9-11, 13, 15-17, 19 (Show (PAQ)T(PAQ)
is similar to ATA – why is this sufficient?) |
|
|
|
4/22/2013, |
Saturn, Classifying
Pictures |
Exciting
applications! |
Work on project 1! |
4/24/2013 |
|
|
4/24/2013,
4/26/2013 |
Cats and Dogs |
Again! |
Work on project 2! |
4/29/2013 |
