Math 224: Linear Algebra I, Fall 2012
Monday, Wednesday, and Friday 10:1011:00am
Pierce Hall L09
Textbook
Linear Algebra, A Modern Introduction,
Third Edition, by David Poole.
Office
Hours (Hayes 309A)
Monday 2:103:00pm
Tuesday
12:101:00pm
Wednesday
11:10am12:00pm
Thursday
9:1011:00am
Dropin
Tutoring with Neil (Sam Mather 202)
Sunday 8:009:00pm
Tuesday 8:009:00pm
Thursday
8:009:00pm
Homework
Lesson 
Date 
Section(s) 
Topic 
Homework 
1 
9/3/2012 
1.1 
The Geometry and Algebra of Vectors 
Section 1.1: #1c, 2c, 3d, 4d, 5bd, 6, 10, 11, 14, 21 Read Syllabus and Section 1.2. 
2 
9/5/2012 
1.1 

Section 1.1: #15, 17, 19, 23, 24 Worksheet (more on exploring
linear combinations) 
3 
9/7/2012 
1.2 
Length and Angle: The Dot Product 
Section
1.2: #5, 11, 15, 17bd, 21, 22, 28 Read
Section 1.3. Think
about: Error worksheet, puzzle, and why we don’t have an associative property
for the dot product. 
4 
9/10/2012 
1.2 

Section
1.2: #40, 41, 43, 49, 50,
60, 61, 70 Study
for quiz 1. 
5 
9/12/2012 
1.3 
Lines and Planes 
Section
1.3: # 7, 10, 13, 15, 16, 22, 23, 35, 43 Read Section 1.4 (Code Vectors
portion) 
6 
9/14/2012 
1.3 

Read
Section 2.1. 
7 
9/17/2012 
1.4 
Code Vectors 
Section
1.4: #23,
25, 28, 30ab, 32, 35 Read
Section 2.2. 
8 
9/19/2012 
2.1 
Systems of Linear Equations 
Section
2.1: #1, 3,
4, 10, 17, 21, 30, 35, 41 
9 
9/21/2012 
2.2 
Solving Linear Systems 
Section
2.2: #1, 3, 5, 7, 11, 13 Read
Section 2.3. We
will continue working on the worksheet on Monday – please work on it over the
weekend and come with questions! 
10 
9/24/2012 
2.2, 2.3 
Spanning Sets and Linear Independence 
Show all steps and use proper notation for all REF/RREF
computations. Sec
2.2: #31
(write solution in vector form), 35,
37, 41
(use REF to find/justify your answer), 45,
47, 49 Section
2.2 worksheet: #2
(note that there are actually 8 different forms, not 7), 6,
7 
11 
9/26/2012 
2.3 

Explain
theorems 13 on handout. Questions
1, 2 from class (about zero vector and 3x3 matrices). 2.3
Worksheet: Questions 1, 2, and 4. Read
Section 2.4 (focus on finite linear games). 
12 
9/28/2012 
2.3/2.4 
Finite Linear Games 
Sec
2.3
(row reduction on computer/calculator okay): #5, 11, 16, 25, 29, 42 2.3
Worksheet: Question 6 Sec
2.4
(row reduce by hand): #29, 31 Play
the Lights Out game at the website below. http://www.whitman.edu/mathematics/lights_out/ Can
you solve it without using linear algebra? How will you set up equations to
solve it using linear algebra? 

10/1/2012 

The Colley Method for Sports Rankings 
Read
Section 3.1. Work
on Project 1! 
13 
10/3/2012 
3.1 
Matrix Operations 
Sec
3.1: #68, 18, 19, 21, 2325, 33, 35 3.1
Worksheet: Questions 1315 You can use Maple to check
your answers, but you should do these problems by hand (the one exception is
#35a, for which you may use Maple.) Read
Section 3.2. 
14 
10/5/2012 
3.2 
Matrix Algebra 
Sec
3.1: #17, 29 Sec
3.2: #4, 5, 9, 15, 19
(follow style of proof of part (b) in textbook), 27,
36 

10/8/2012 

Projects/SampleODK1 
Study
for ODK 1 (Sec 1.1 – Sec 3.2)! 
15 
10/15/2012 
3.3 
The Inverse of a Matrix 
Write
in your own words the portion (a)→(b) →(c) →(d) of the proof of Thm 3.12. Sec 3.3: #3 (use formula
in Thm 3.8), 11, 16 (don’t use components! This
should be a very short proof.), 19,
22, 39, 53, 61, 65, 71 Read
Sections 3.3 and 3.5. 
16 
10/17/2012 
3.5 
Subspaces, Basis, Dimension, and Rank 
Sec
3.5: 3, 715 (the proof for #9 should be short!),
57 
17 
10/19/2012 
3.5 

Sec
3.5: 17, 18, 20, 21, 25, 27, 29, 34, 39 
18 
10/22/2012 
3.5 

Sec
3.5: 38, 4143, 47, 51, 52, 55 Prove
Theorem 3.29 (try to do it on your own without the textbook first). Challenge Problems: 59, 60 (for a fun, enlightening and
completely voluntary challenge). Read
Section 3.6. 
19 
10/24/2012 
3.6 
Introduction to Linear Transformations 
Sec
3.6: 1, 2, 4, 10, 11, 13, 15, 17, 18, 44, 45 
20 
10/26/2012 
3.6 

Sec
3.6: [due Monday] #21, 23, 33, 37, 40, 54 Hint:
For #54, show that both range(T) and col([T]) are
equal to span(T(e_{1}),…,T(e_{n})). Challenge
Problem:
42 Linear
transformations worksheet (Matlab): [due Friday] 
21 
10/29/2012 
4.1 
Introduction to Eigenvalues and Eigenvectors 
Read
Sec 4.1. Sec
4.1: 5, 13, 16, 2022, 23, 25, 27, 31 Challenge
Problem:
35 Start
reading Sec 4.2. 
22 
10/31/2012 
3.6 

Finish
Matlab linear transformation homework. Sec
3.6: 4649. Read
Sec 4.2. 
23 
11/2/2012 
4.2 
Determinants 
Sec
4.2: #1, 5, 15, 20, 22 (see Example 4.13), 35,
37, 39 Read
Sec 4.3. 
24 
11/5/2012 
4.2 

Sec
4.2: #23, 27, 29, 32, 33, 49, 51, 53, 54 Challenge
Problem:
42 Work on projects! 
25 
11/7/2012 
4.3 
Eigenvalues and Eigenvectors of n x n Matrices 
Sec
4.3: #7, 19, 21, 24, 25 Finish
questions 4 and 5 on the worksheet. Work on projects! 
26 
11/9/2012 
4.3 

Sec
4.3: #17, 18, 34, 35 Attempt
questions 9 and 10 from the worksheet. Work on projects and review material! 
27 
11/26/2012 
4.4 
Similarity and Diagonalization 
Sec
4.4: #14, 32 (you can use Sec 3.5 #61 as given; it is recommended as a
challenge problem if you haven’t done it), 40, 45, 46 Read
Sec 4.4. 
28 
11/28/2012 
4.4 

Sec
4.4: #7, 15, 29, 37, 42, 43, worksheet
problems #5, 710 (Problems
above and projects are due Monday.) Read
Sec 5.1 for Friday. 
29 
11/30/2012 12/3/2012 
5.1 
Orthogonality in R^{n}^{} 
Sec
5.1: #1, 6, 10, 13, 18,
19 (for #18 and #19, compute QQ^{T} or Q^{T}Q!), 2224, 27 You
are encouraged to read/understand/reproduce the proof of Theorem 5.6. Read
Sec 5.2. 
30 
12/5/2012 
5.2 
Orthogonal Complements and Orthogonal Projections 
Worksheet
questions: #4, 5 Sec
5.2: #3, 5, 7, 9, 13, 17, 23, 24 Read
Sec 5.3. 
31 
12/7/2012 
5.2, 5.3 
The Orthogonal Decomposition Theorem, The GramSchmidt Process and the QR Factorization 
Worksheet
question: #6 Find
the Error Worksheet. Sec
5.2: #21, 22 (what does your answer imply?), 27, 28 Sec
5.3: #10, 12, 16, 19 Computations for this problem set should be done by hand. Read
Sec 5.4 
32 
12/10/2012 
5.4 
Orthogonal Diagonalization of Symmetric Matrices 
Read
the statement of the Spectral Theorem. Make
decent attempts at worksheet questions 6 and 7. 
33 
12/12/12! 
5.4, Review 

Worksheet
questions 3 and 4. Sec
5.4: #8, 13, 15, 20, 23 Challenge
Problem:
26 Feel free to use Maple to do computations such as finding
characteristic polynomials, row reducing, multiplying matrices, etc. (but you
should be prepared to do these computations by hand on the final ODK). 