MA2330: Introduction to Linear Algebra

Course description

An introduction to linear algebra and how it can be used, including basic mathematical proofs. Topics include systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem. Not open to students with credit in MA2320 or MA2321. Course prerequisite is any math class numbered MA1090 or higher.

Credits: 3.0

Lec-Rec-Lab: (0-3-0)

Semesters Offered: Fall, Spring

Pre-Requisite(s): MA 1160 or MA 1161

Text

David C. Lay Linear Algebra and its applications, (Fourth Edition)

Tentative Schedule.

Linear equations in Linear Algebra

Date

Topic

Homework exercises

Due

HW 1

Due

Jan 13

1.1 Systems of Linear Equations

6, 10, 14, 20, 24, 26

Jan 22

Jan 15

1.2 Row Reduction and Echelon Form

4, 8, 12, 14, 20, 22, 24, 26

Jan 22

Jan 17

1.3 Vector Equations

10, 12, 14, 16, 18, 22, 24, 28

Jan 22

HW 2

Due

Jan 20

MLK DAY - No class

Jan 22

1.4 The Matrix Equation Ax=b

4, 8, 10, 12, 16, 18, 22, 26, 38

Jan 29

Jan 24

1.5 Solutions Sets of Linear Equations

2, 6, 8, 12, 14, 18, 34, 38

Jan 29

HW 3

Due

Jan 27

1.7 Linear Independence

6, 8, 10, 12, 18, 24, 28, 30, 32, 38

Feb 3

Jan 29

1.8 Introduction to Linear Transformations

4, 6, 12, 20, 24, 30, 32

Feb 3

Jan 31

1.9 The Matrix of a Linear Transformation

2, 16, 20, 24, 26

Feb 3

Review

Feb 4

Chapter 1 Evening Exam 1

Feb 5

No class - Makeup for Exam 1

Feb 7

Winter carnival recess

Matrix Algebra

HW 4

Due

Feb 10

2.1 Matrix Operations

2, 8, 12, 16, 20, 22, 26, 28

Feb 19

Feb 12

2.2 The inverse of a matrix

8, 11, 16, 20, 23, 24, 30, 32

Feb 19

Feb 14

2.3 Characterizations of Invertible matrices

2, 6, 14, 20, 22

Feb 19

HW 5

Due

Feb 17

2.5 Matrix Factorization

2, 4, 8, 10, 12

Feb 26

Feb 19

PA=LU decomposition

Read LU.pdf and do exercises 1, 2

Feb 26

Determinants

Feb 21

3.1 Introduction to Determinants

3.2 Properties of Determinants

(3.1)4, 6, 10, 16, 20,22, 44

(3.2) 6, 12, 16, 18, 26, 28, 31, 34

Feb 26

Recommended exercises

Feb 24

3.3 Cramer's rule, Vol. and Linear Trans.

4, 6, 8, 12, 18, 22

Feb 26

Review for Chapter 2 and 3 evening Exam 2

Feb 27

Chapter 2 and 3 evening Exam 2

Vector Spaces

HW 6

Due

Mar 28

4.1 Vector Spaces and Subspaces

2, 6, 8, 12, 14, 16, 18, 22

Mar 18

Mar 2

4.2 Null Spaces, Col. Space and Lin. Trans.

4.3 Linear independent sets ; Bases

(4.2) 2, 4, 8, 10, 12, 14, 18, 22, 24

(4.3) 2, 6, 10, 12, 14, 16, 20, 22, 24, 25

Mar 18

Mar 4

4.4 Coordinate Systems

2, 6, 10, 14, 23, 34

Mar 18

Mar 6

No class - makeup for Exam 2

Mar 9

Spring break

Mar 11

Spring break

Mar 13

Spring break

HW 7

Due

Mar 16

4.5 The Dimension of a vector space

2, 6, 8, 12, 16, 22, 24, 26, 30

Mar 25

Mar 18

4.6 Rank

4, 6, 8, 12, 16, 19, 22, 28, 29

Mar 25

Mar 20

4.7 Change of Bases

2, 4, 6, 8, 10, 14

Mar 25

Mar 23

Review for Chapter 4 evening Exam 3

Mar 24

Chapter 4 evening Exam 3

HW 8

Due

Mar 25

5.1 Eigenvectors and eigenvalues

2,4,6,8,10,12,14,20

Apr 1

Mar 27

5.2 The Characteristic equation

2,4,8,10,14,20,22

Apr 1

Eigenvalues and Eigenvectors

HW 9

Due

Mar 30

5.2 The Characteristic equation

2,4,8,10,14,20,22

Apr 8

Apr 1

5.3 Diagonalization

2,4,6,8,20,22,26

Apr 8

Orthogonality and Least Squares

Apr 2

6.1 Inner Product Length and Orthogonality

2,4,6,8,14,18

Apr 8

HW 10

Due

Apr 6

6.2 Orthogonal sets

2,6,8,16,20,22,24

Apr 15

Apr 8

6.3 orthogonal projection

2,4,6,10,12,14,20

Apr 15

Apr 10

6.5 Least-squares problems

2,4,6,10,12,14

Apr 15

Recommended exercises

Apr 13

6.6 Applications to linear models

2,4,8,10

Apr 15

T.B.A.

Apr 22

T.B.A.

Apr 20

Review

Apr 22

Chapter 5 and 6 Take home Exam due

Apr 24

No class Make up for Exam 4.)

Apr 27

Exam Week

Apr 29

Exam Week

Apr 27

Exam Week

You are responsible for all of the material in these sections even if it is not presented in class.

Homework

You may work together on homework, but be sure you understand the exercises yourself. Although all assigned exercises must be turned in on there due date, we will in fact only grade a portion of them.

Grading

Your grade will be based on

Homework (25%)
Four examinations lowest score dropped (45%)
The first 3 of these exams will be 1-hour exams given in a 2 hour evening time slot.
The fourth exam will be a take home exam.
A 2-hour comprehensive final (30%).

(From the assigned home work a smaller number of problems will be graded. Recommended exercises are not to be handed in.)

Some advice

This course in Linear Algebra will likely be your first introduction to abstract axiomatic mathematics. This approach may seem very unfamiliar at first and your performance will depend heavily on how much effort you put into understanding the concepts. At a minimum you should

Attend all lectures.
Review each lecture afterwards - aiming for understanding.
Attempt all exercises by yourself.
Work through odd numbered exercises with other students in the class. Solutions to odd numbered exercises are at the end of the textbook.
Read any course related material.