Math 215

LINEAR ALGEBRA

Fall 2008

Topics and Lectures

**Chapter 1**

1.1 Systems of Linear Equations
Lecture 1.1

HW (pp 11-13) 2, 6, 12, 13, 16, 19, 23, 24. Due Mon. Sept. 15

1.2 Row Reduction and Echelon Forms
Lecture 1.2

HW (pp 25-26) 2, 4, 7, 8, 12, 14, 19. Due Wed. Sept. 17

1.3 Vector Equations
Lecture 1.3

HW (pp. 37-39) 6, 9, 12, 14, 18, Due Mon. Sept. 20

1.4 The Matrix Equation Ax = b
Lecture 1.4

HW (pp. 47- 48) 2, 4, 8, 11, 12, 13, 14, 21, 24 Due Fri. Sept. 26

1.5 Solution Sets of Linear Systems
Lecture 1.5

HW (pp. 55-56) 2, 6, 8, 10, 12, 16, 24 Due Mon. Sept. 29

1.7 Linear Independence
Lecture 1.7

HW (pp. 71-72) 2, 6, 8, 12, 22, 26, 28 Due Wed. Oct. 1

1.8 Introduction to Linear Transformations
Lecture 1.8

HW (pp. 79-81) 4, 6, 10, 12, 22 Due Mon. Oct. 6

1.9 The Matrix of a Linear Transformation
Lecture 1.9

HW (pp. 90-91) 2, 4, 6, 18, 24 Due Wed. Oct. 8

**Chapter 2**

2.1 Matrix Operations
Lecture 2.1

HW (pp. 116-117) 2, 6, 10, 12, 16 Due Fri. Oct. 10

2.2 The Inverse of a Matrix
Lecture 2.2

Hw (pp. 126-127) 2, 4, 6, 12, 16, 22, 28 Due Mon. Oct. 20

2.3 Characterizations of Invertible Matrices Lecture 2.3 Hw (pp. 132-133) 2, 4, 6, 12, 16, 22, 28 Due Fri. Oct. 24

2.8 Subspaces of R^n
Lecture 2.8
Know how to do: 1-26

Hw (pp. 173-174) 2, 8, 10, 16, 18, 22, 26 Due Wed. Oct. 29

2.9 Dimension and Rank
Lecture 2.9
Know how to do 1-25

Hw (pp.180-182) 2, 6 10, 12, 14, 18, 24 Due Fri. Oct. 31

**Chapter 3**

3.1 Introduction to Determinants

Know how to do 1-40

Hw (pp. 190-191) 2, 6, 10, 12, 22, 24, 40 Due Wed. Nov. 5

3.2 Properties of Determinants
Lecture 3.1 and 3.2

Know how to do 1-28

Hw (pp. 199-200) 2, 4, 6, 8, 12, 16, 22, 24, 28 Due Fri. Nov. 7

3.3 Cramer's Rule, Volume, and Linear Transformations
Lecture 3.3 Cramer

Lecture 3.3 Area

Know how to do 1- 22

Hw (pp. 209-210) 4, 6, 12, 20 Due Mon. Nov. 10

**Chapter 4**

4.1 Vector Spaces and Subspaces Lecture 4.1

4.2 Null Spaces, Column Spaces, and Linear Transformations Lecture 4.2

4.3 Linearly Independent Sets: Bases Lecture 4.3

4.5 The Dimension of a Vector Space Lecture 4.4

4.6 Rank Lecture 4.6

4.7 Change of Basis Lecture 4.7

**Chapter 5**

5.1 Eigenvectors and Eigenvalues Lecture 5.1

5.2 The Characteristic Equation Lecture 5.2

5.3 Diagonalization Lecture 5.3

5.4 Eigenvectors and Linear Transformations

**Chapter 6**

6.1 Inner Product, Length, and Orthogonality Lecture 6.1

6.2 Orthogonal Sets Lecture 6.2

6.3 Orthogonal Projections Lecture 6.3

6.4 The Gram-Schmidt Process Lecture 6.4

Exam I

100 pts Friday Oct. 10

Exam II

100 pts Friday Nov. 21

Final Exam

200 pts

Section 01 Friday Dec. 19

11:30 am - 2:30pm

Section 02 Thurs. Dec. 18

7:00 pm - 10:00pm

Homework/Quizzes

100 pts

Projects

100 pts

Total Points 600 pts

A ... 100% - 90%

B ... 89% - 80%

C ... 79% - 70%

D ... 69% - 60%

F ... 59% - 0%

+/- Grades may be given for borderline percentages

To compute your grade,

(your total points)/6