WORCESTER POLYTECHNIC INSTITUTE

MATHEMATICAL SCIENCES DEPARTMENT

 

 

MA2071 - Matrices and Linear Algebra 1

Term Bí98 - 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, 6th edition,

Prentice Hall

 

Course Goals:

    1. Learn the language and methods of linear algebra.
    2. Develop an appreciation for abstraction and mathematical rigor.
    3. Appreciate the power of linear algebra to solve real-world problems.
    4. Apply technological tools as an aid to computation.
    5. 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 R2 and Rn

 

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