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.

 

Syllabus

 

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 donít 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

 

Worksheet

Read Section 2.1.

7

9/17/2012

1.4

Code Vectors

Section 1.4: #23, 25, 28, 30ab, 32, 35

Worksheet

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 Ė 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 Ė 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 (donít 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),Ö,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 havenít 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).