Course Title: Linear Algebra
Course Number: Ma 260
Reference Number: 1974
Prerequisite: Calculus II
Semester: Spring 2010
Instructor: Dr. Beimnet Teclezghi
Tele: 201-200-3139; E-mail bteclezghi@njcu.edu
Office Hrs: M 11:00 -11:50 A.M., T 11;00- 11:50 A.M., 4:00 .-6:50 P.M., R 11:00- 11:50 A.M.
Office: K 528
Text: Larson, Edwards, Falvo Elementary Linear Algebra, 6th ed., Houghton Mifflin, New York 2009.
Course description: Algebra of Matrices and Vector Spaces and applications to
Solutions of systems of linear equations and geometric
Transformations are studied in this course.
To introduce different methods of solving systems of linear equations
Using Matrices and representation of geometric transformations by means
of matrices.
Goals:
Objectives/outcomes: At the end of this course the successful student will be familiar with the
Procedure: .
ideas of matrices and their applications in solving problems involving systems
of linear equations and linear programming problems. Also he/she will be
capable of representing geometric transformations by means of matrices and to
express the volume of certain figures and equation of line using determinants.
. Lecture/discussion
. Use of graphing calculators
. Use of available software
Course content and course Calendar:
I. Systems of Linear Equations (week I )
1. Introduction to Systems of Linear equations
2. Gaussian Elimination and Gauss Jordan Elimination
3. Application of Systems of Linear Equations
II. Applications of Systems of equations and Matrices (Weeks II- IV )
1. Application of Systems of Linear Equations Continued
2. Operations with Matrices
3. Properties of Matrix Operations
4. The Inverse of a Matrix
5. Elementary Matrices
6. Application of Matrix operation
III. Determinants and their Applications (weeks V- VII)
1.The Determinant of a Matrix
2. Evaluation of a Determinant using Elementary Operations
3. Properties of Determinants
4. Introduction of Eigenvalues
5. Applications of Determinants
IV. Vector Spaces (Weeks VIII-X)
1. Vectors in R n
2.
3.
4.
5.
6.
7.
8.
3.
Vector Spaces
Subspaces of Vector Spaces
Spanning Sets and Linear Independence
Bases and Dimension
Rank of a Matrix and Systems of Linear Equations
Coordinates and change of Basis
Application of Vector Spaces
V. Inner Product Space (Weeks XI-XII)
n
1. Length and Dot Product in R
2.
3.
4.
5.
Inner Product Space
Orthonormal Basis: Gram-Schmidt Process
Mathematical Models and Least Square Analysis
Application of Inner Product Space
VI. Linear Transformations (Weeks XIII - XIV)
1. Introduction to Linear Transformations
2. The Kernel and Range of a Linear Transformation
3. Matrices for Linear Transformations
4. Transition Matrices and Similarity
5. Application of Linear Transformations
VI. Bibliography
Linear Algebra With applications, 4th ed., Prentice Hall, New Jersey 2002
.
VIII. Course Evaluation:
There will be 10-12 daily quizzes out of which 10 will be considered.
Three tests and a comprehensive final exam will be given
Quizzes and home works
100 points
Two Tests
200 points
Final exam
200 points
Total
500 points
Quizzes will be given at the beginning 10 min of class. All tests will be
announced one week in advance. No make up quiz will be given. There will not
be makeup tests unless there is valid reason.
IX. Grading Criteria:
Possible Grades: , A, A-, B+, B, B-, C+, C, C-, D, and F
Let G be your average over the whole semester work.
G>=92
88<= G < 92
84 <= G < 88
78 <= G < 84
74<= G < 78
A
AB+
B
B-
70<=G < 74
C+
68<= G < 74
65<=G < 68
60 <=G< 65
G< 60
C
CD
F
Attendance Policy: Any student who is absent for 6 or more contact hours will
automatically receive a grade F for the course.