Math 52: Linear Algebra David Dumas Brown University Fall 2005

 A picture of a 428x428 Hadamard matrix, i.e. a matrix with orthogonal columns and all entries equal to +1 (white pixels) or -1 (black pixels). This example was discovered H. Kharaghani and B. Tayfeh-Rezaie in 2004, and was the first of size 428x428. It is not known if there is a 668x668 Hadamard matrix, though it is conjectured that examples of size 4nx4n exist for all n. See the Wikipedia article for further discussion.

General Information

Text Office Introduction to Linear Algebra, Third Edition, by Gilbert Strang, ISBN 0961408898 Kassar House 114 401-863-7957 Wed 12:30-1:30pm, Thurs 2:30-3:30pm, and by appointment Section 1: MWF 2:00 - 2:50 PM (G hour) Section 2: TR 1:00 - 2:20 PM (J hour) Section 1: Barus & Holley 160 Section 2: Barus & Holley 155 One problem set will be assigned each week. Typically assignments will be given on Thursdays or Fridays (depending on the section) and collected one week later. Late homework will NOT be accepted. There are no exceptions to this policy. The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!

Handouts

All homework problems and readings are from the textbook, Introduction to Linear Algebra, Third Edition, by Gilbert Strang.
• 2005-09-06 - Read Chapters 1 and 2 (with less emphasis on section 1.2)
• 2005-09-08 - Homework 1 - Due Thursday 2005-09-15 (Section 2), Friday 2005-09-16 (Section 1):
```1.1.26  1.1.28  2.1.13  2.1.27  2.2.11
2.2.12  2.2.19  2.3.1   2.3.3   2.3.27
```
• 2005-09-15 - Read Sections 3.1-3.2
• 2005-09-15 - Homework 2 - Due Thursday 2005-09-22 (Section 2), Friday 2005-09-23 (Section 1):
```2.4.1  2.4.13  2.5.7  2.5.10  2.6.11
2.7.1  2.7.22
```
• 2005-09-22 - Read Section 3.3
• 2005-09-22 - Homework 3 - Due Thursday 2005-09-29 (Section 2), Friday 2005-09-30 (Section 1):
```*3.1.4   *3.1.9   3.1.10  *3.1.17  3.1.19
3.1.25   3.1.28  3.2.1    3.2.23  3.2.26
```
The problems that were originally part of Homework 2 are marked with "*".
• 2005-09-28 - Read Sections 3.4-3.5
• 2005-09-29 - Homework 4 - Due Thursday 2005-10-06 (Section 2), Friday 2005-10-07 (Section 1):
```3.2.2  3.2.3  3.2.4
3.2.9  3.3.1  3.3.2
```
• 2005-10-06 - Read Section 3.6
• 2005-10-06 - Homework 5 - Due Thursday 2005-10-13 (Section 2), Friday 2005-10-14 (Section 1):
```3.3.8  3.3.10  3.4.1  3.4.4
3.4.6  3.4.32  3.5.1  3.5.41
```
• 2005-10-13 - Read Sections 4.1-4.2
• 2005-10-13 - Homework 6 - Due Thursday 2005-10-20 (Section 2), Friday 2005-10-21 (Section 1):
```3.5.2  3.5.5  3.5.11 3.5.14
3.5.21 3.5.24 3.6.2  3.6.3
```
• 2005-10-20 - Read Sections 4.3-4.4
• 2005-10-20 - Homework 7 - Due Thursday 2005-10-27 (Section 2), Friday 2005-10-28 (Section 1):
```3.6.7  3.6.13  3.6.14  4.1.5
4.1.14 4.1.22  4.2.1   4.2.16
```
• 2005-10-26 - Read Sections 5.1-5.2
• 2005-10-27 - Homework 8 - Due Thursday 2005-11-03 (Section 2), Friday 2005-11-04 (Section 1):
```4.2.13 4.2.19 4.3.1  4.3.9  4.4.3
4.4.11 4.4.23 5.1.1  5.1.2
```
• 2005-10-31 - Read Section 5.3
• 2005-11-03 - Read Section 6.1
• 2005-11-03 - Homework 9 - Due Thursday 2005-11-10 (Section 2), Friday 2005-11-11 (Section 1):
```5.1.13 5.1.28 5.2.2 5.2.12
5.3.1  5.3.6  5.3.21
```
• 2005-11-10 - Read Section 6.2
• 2005-11-10 - Homework 10 - Due Thursday 2005-11-17 (Section 2), Friday 2005-11-18 (Section 1):
```5.3.19  5.3.22 6.1.5  6.1.6  6.1.13
6.1.20  6.2.1  6.2.5  6.2.9
```
• 2005-11-16 - Read Sections 6.3 - 6.4
• 2005-11-17 - Homework 11 - Due AFTER THANKSGIVING, Tuesday 2005-11-29 (Section 2), Monday 2005-11-28 (Section 1):
```6.2.8 6.2.15 6.2.16 6.2.20
6.3.3 6.3.4  6.3.19 6.3.23
```
• 2005-11-21 - Read Sections 6.5 - 6.6
• 2005-11-28 - Read Sections 7.1-7.2, also examine the table on p. 362
• 2005-11-28 - Homework 12 - Due at the LAST LECTURE, Tuesday 2005-12-06 (Section 2), Monday 2005-12-05 (Section 1):
```6.3.24  6.4.3  6.4.5  6.4.21  6.5.2
6.5.10  6.5.12 6.6.3  6.6.17
```
• 2005-12-5 - Homework 13 will not be collected; these are suggested review problems that cover material from 7.1 and 7.2:
```7.1.3  7.1.6  7.1.12
7.2.5  7.2.6  7.2.21
7.2.22 7.2.29 7.2.33
```
Also check the answer key for homework 13.

Important Dates

There will be two in-class one-hour exams and a final exam. The registrar determines the date and time of the final exam, and these cannot be changed. You must be available on Monday, December 19, to take the final exam.
Exam 1 Exam 2 Fri, Oct 7 (Section 1)Thurs, Oct 6 (Section 2) In class Wed, Nov 9 (Section 1)Tues, Nov 8 (Section 2) In class Thurs, Dec 8, 1:00-2:20pm Barus and Holley 141 Wed, Dec 14, 1:00-2:20pm Barus and Holley 141 Mon, Dec 19, 2-5pm (Both sections) Sayles Hall Auditorium