WORCESTER POLYTECHNIC INSTITUTE

MATHEMATICAL SCIENCES DEPARTMENT

MA2071 - Matrices and Linear Algebra 1

Term B’98 - October 28 - December 18

**Instructor:** Professor Peter R. Christopher Office: SH 305B

email: peterrc@wpi.edu Telephone: 831-5269

Office Hours: Monday, Friday - 9:00-10:00am

Tuesday - 3:00-4:00pm or by appointment.

**Teaching Assistant:** Elena Volkova, Office: SH 205

email: volkova@wpi.edu

Office Hours: Thursday - 3:00-4:00pm

**Peer Learning Assistants: **Sharad Bhojnagarivola (sharad)

Kevin Dickert (kad)

Adam Howes (ahowes)

Jen Hardy (jehardy)

Joseph Laws (cinnamon)

Jen Marinello (jmari)

Jeremy Proulx (zear)

**Class Hours: **MTRF - 8:00-8:50am, Perrault Hall

**Conference Sessions: **Section 1 Wed. 8:00-8:30 SH308

Section 2 Wed. 12:30-1:20 SH309

Section 3 Wed. 12:30-1:20 SH304

Section 4 Wed. 8:00-8:50 SH106

**Text:** B. Kolman; Introductory Linear Algebra with Applications, 6^{th} edition,

Prentice Hall

Course Goals:

- Learn the
__language__and__methods__of linear algebra. - Develop an appreciation for
__abstraction__and mathematical rigor. - Appreciate the power of linear algebra to solve
__real-world__problems. - Apply technological
__tools__as an aid to computation. - Improve
__research__and__communication__skills by working cooperatively in teams.

Grades and Requirements

Grades of A, B, C for scores in the 90s, 80s or 70s respectively will be determined as follows:

__ACTIVITY__ __% POINTS__

Test I 30

Test II 30

Computer Projects 15

Class Quizzes/Homework 20

Conference Quizzes __5__

Total 100

Computer Projects

Four Computer Projects are scheduled as team activities. Each 3-person team will submit one report, signed by all team members, per project.

Homework

The suggested homework problems are listed on the syllabus. Completing these exercises is essential to your mastery of the material. Homework is your responsibility, the syllabus problems will not be collected. However, quiz problems will often resemble homework problems. We may require you to pass in special homework problems, assigned with advanced notice.

Quizzes

We will have a 20 minute quiz in class on Fridays (except on 10/30). The lowest quiz score will be dropped. PLAs will also administer 5-10 minute quizzes during conference.

Tests

The two tests scheduled on the syllabus page will be given in class.

Conferences

Participation in conferences is required. In these sessions you will be actively participating in small groups in a cooperative learning environment. The PLAs are there to help you solve problems, rather than to solve problems for you.

MA 2071 - MATRICES AND LINEAR AGLEBRA I

SYLLABUS

You should complete the following exercises as each topic is covered. Please keep aware of possible changes, additions to, or omissions from the following list of topics, recommended exercises and scheduled activities.

Chapter 1 Linear Equations and Matrices

1.1 Linear Systems p.9 1, 5, 9, 11, 15, 19, 21, 23

1.2 Matrices p.16 3, 5d, 8, 7b

1.3 Dot Product and Matrix Multiplication p.30 3, 5d, 7c, 9, 13, 15, 21a, 27, 29

1.4 Properties of Matrix Operations p.44 3, 9c, 11, 15, 19, T.10, T.21

1.5 Solutions of Linear Systems of Equations p.65, 1, 3, 9a,c, 11, 19, 21, 23, T.11

1.6 The Inverse of a Matrix p.83 3, 5b, 9a, 11, 18, 21, 25, T.8

Chapter 2 Determinants

2.1 Definition and Properties p.100 11, 13, 15a,b, T.3, T.6

2.2 Cofactor Expansion and Applications p.115 3a, 15a, 19a

Chapter 3 Vectors in R^{2} and R^{n}

3.1 Vectors in the Plane p.139 7a, c, 11, 13, 17

3.2 Vectors in n Dimensions p.155 1b, 13b, 15, 21b, 25, 27a, 35

3.3 Introduction to Linear Transformations p.169 1, 13, 17, 21, 23

3.6 Lines and Planes p.192 3, 5a, 6a, 9a, 10a, 11a, 17, 19

Test I Thursday, November 19

Chapter 4 Real Vector Spaces

4.1 Real Vector Spaces p.202 1, 3, 4, 11, 15, 17

4.2 Subspaces p.210 1, 5, 11, 15, 18, 21, 23, T.7

4.3 Linear Independence p.222 5, 7, 9, 10, 12, 15, T.2, T.5

4.4 Basis and Dimension p.234 3, 5, 9, 11, 13, 19, 25, 27, T.3

4.5 Homogeneous Systems p.243 1, 5, 9, 13, 17

4.6 Rank of a Matrix p.253 1, 3, 7, 11, 17, 25, 31

4.7 Change of Basis p.265 1, 2, 3, 9, 11, 13, 15, 19, 23

4.8 Orthonormal Bases p.275 1b, 2a, 3, 5, 11, 15, 19

Chapter 5 Eigenvalues and Eigenvectors

5.1 Diagonalization p.310 1, 9, 11, 19, 23, 25, 26, T.3, T.6

5.2 Diagonalization of Symmetric Matrices p.322 1, 2b, 9, 11, 13, 17, T.1, T.4

Test II Thursday, December 17

Project Schedule

Project 1 Assigned Monday, Nov. 9

Due Monday, Nov. 16

Project 2 Assigned Monday, Nov. 16

Due Monday, Nov. 23

Project 3 Assigned Monday, Nov. 30

Due Monday, Dec. 7

Project 4 Assigned Monday, Dec. 7

Due Monday, Dec. 14