Math 324 Linear Algebra II
Monday, Wednesday, and Friday 9:1010:00am
Hayes Hall 203
Textbook
Linear Algebra, A Modern Introduction, Third Edition, by David Poole.
Office Hours (Hayes 309A)
Monday 2:103:00pm
Tuesday
11:10am1:00pm
Wednesday
2:103:00pm
Thursday
10:1011:00am
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 that is as
small as possible. Section 6.1: #4, 17, 18 (just show that axioms 1 and 6 hold), 22, 23, 38, 53, 5557, 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 
6.46.5 
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, 911, 13, 16, 18, 20, 21, 27, 32 7.0
Taxicab: #68 Worksheet
on Read
Section 7.2. Challenge Problem: Prove that proj_{W}(v) and perp_{W}(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: #24, 79, 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, 5355 
3/27/2013 
10 
3/25/2013,
3/27/2013 
7.4 
The Singular
Value Decomposition! :) 
Section
7.4: #11, 15, 18, 19, 21, 2430,
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 A^{T}A),
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 
Inclass
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. 646647: 1
(b)(d), (h)(j), 26, 7 or 8, 911, 13, 1517, 19 (Show (PAQ)^{T}(PAQ)
is similar to A^{T}A – 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 