Math 224: Linear Algebra I, Fall 2012
Monday, Wednesday, and Friday 10:10-11:00am
Pierce Hall L09
Textbook
Linear Algebra, A Modern Introduction,
Third Edition, by David Poole.
Office
Hours (Hayes 309-A)
Monday 2:10-3:00pm
Tuesday
12:10-1:00pm
Wednesday
11:10am-12:00pm
Thursday
9:10-11:00am
Drop-in
Tutoring with Neil (Sam Mather 202)
Sunday 8:00-9:00pm
Tuesday 8:00-9:00pm
Thursday
8:00-9:00pm
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 1-3 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: #6-8, 18, 19, 21, 23-25, 33, 35 3.1
Worksheet: Questions 13-15 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, 7-15 (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, 41-43, 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(e1),…,T(en)). 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, 20-22, 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: 46-49. 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: #1-4, 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, 7-10 (Problems
above and projects are due Monday.) Read
Sec 5.1 for Friday. |
|
29 |
11/30/2012 12/3/2012 |
5.1 |
Orthogonality in Rn |
Sec
5.1: #1, 6, 10, 13, 18,
19 (for #18 and #19, compute QQT or QTQ!), 22-24, 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 Gram-Schmidt 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). |