Course Content
Spring-2024
INSTITUTE OF MATHEMATICS
Khwaja Fareed University of Engineering and Information Technology,
Rahim Yar Khan
Course Code: MATH-2103 Course Title:
Linear Algebra
Credit Hours: 03 Maximum Lectures:
32 (1.5 hours each)
Course Type: Pre-requisites: None
Year: 2024 Semester: Spring-2024
Instructor’s Name: Dr. Shah Jahan Office (Room No):
MEEN-2.21DR, Institute of
Mathematics,Mechanical
Engineering Building, KFUEIT,
RYK
E-mail: jahanshah@kfueit.edu.pk Students’ Contact hours: Students are
welcomed in VISITING HOURS during
office hours to visit my office; however,
30 minutes after every class is reserved
for the students of this class.
Class Level: BS-INFT-3A Institute: Mathematics
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ATTENDANCE POLICY:
As per University policy, a minimum of 75% attendance shall be required for a student to be
eligible to appear in the End Term examinations. All students concerned are advised to keep in
touch with their attendance records through their KFUEIT email account. However, from time to
time instructions during the Spring-2024 semester from competent authority regarding
attendance will be followed as well, strictly.
The students with less than 75% attendance shall not be allowed to take classes after Mid Term
Examination dates (if the case may be).
CLASS RULES AND REGULATIONS:
Without registration and student ID card no student shall be allowed to attend the class. Students
are advised to display the KFUEIT card in a visible position.
The class shall be started as per the given timetable. No one shall be allowed after 5-10 Minutes
of the commencement of class unless genuine excuse.
Students are encouraged to interrupt by asking questions during the lecture.
Drinking, smoking, mobile usage, sectarian or political discussion, and immoral/unethical
activities shall not be allowed during class.
TEACHING & EVALUATION METHODOLOGY:
CLASS LECTURER:
1. English shall be the language of instruction; however, shy or scrawny students shall be
allowed to communicate in Urdu.
2. Each lecture shall be of 1.5 hours and 2 hours (for 3 and 4 CH respectively).
3. Audio video aids like Computer(s), Multimedia, and White Board shall be used as
teaching tools.
4. Students brainstorming
STUDENT’S EVALUATION (GRADING):
The course shall be evaluated out of 100 Marks as per the following division:
GRADING DETAIL:
Seasonal Work (25 Marks):
Quiz: 05 marks
Presentation/Project 10 marks
Assignments 10 marks
Total: 25 Marks
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Mid-Term Examinations (25 Marks):
Short, Long questions
End-Term Examination (50 Marks):
Short, Long questions
OBJECTIVES:
This course is designed as an introduction to linear algebra by emphasizing the geometric significance of the subject.
Student will specially see the vectors in 2 and 3 dimensions geometrically. The objective of the course is to provide a
rigorous approach towards the solutions of linear models which involves more than one variable. The techniques
discussed in this course can be implemented on a wide range of applications from physical world. The matrix algebra
will be helpful in performing and understanding of matrix computations on a machine. The concept of basis for the
solution space helps to describe the good basis for the solution space. The eigenvalues, eigenvectors, inner product
spaces, orthogonality are useful concepts for the analysis of dynamical systems.
COURSE LEARNING OUTCOMES:
On successfully completion of this course, the students will be able to:
1. Solve linear equations using elementary operations.
2. Work with matrix algebra, including matrix inverses and determinants.
3. To use the concepts of subspace, basis and dimension.
4. To construct the “good” basis for the solution spaces and apply the concept on linear models
5. Compute and apply Eigenvalues and Eigenvectors.
6. To construct the orthogonal and orthonormal basis.
COURSE OUTLINES:
System of Linear Equations: System of algebraic equations, Representation in matrix form,
Matrices, Operations on matrices, Echlon and reduced echelon form, Inverse of a matrix by
elementary row operation, solution of linear system by guass Jordan method, guassian elimination
and cramer’s rule, application of linear system
Vector and matrix equation: Introduction to vectors, linear combination, matrix equation, solution
of homogeneous and non homogeneous system of equations, Linear independence, Linear
transformation, matrix of a linear transformation, matrix factorization(LU decomposition)
Determinants: Introduction to determinants, properties of determinants.
Vector Space: Vector space and subspace, bases, null space, column space, diemension of a vector
space, rank
Eigen values and eigen vectors: Eigen values and eigen vectors, characterstic equation,
diagonalization, dynamical system
Orthogonality: inner product, lenth and orthogonality, orthogonal sets, orthogonal projections, the
gram Schmidt process, cayley Hamilton theorem and application.
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Text Books:
1. David C. Lay, Linear Algebra, 5th Edition, Addison-Wesley.
2. Howard Anton, Chris Rorres, Elementary Linear Algebra, 11th edition, Wiley
Recommended Books:
1. S. Lipschutz, M. Lipson, “Schaum’s outline Linear Algebra”, 3rd edition, McGraw Hill 2005.
2. David C. L., Steven R. L., Judi J. M., Linear Algebra and its Applications, 5th Edition, Addison-
Wesley, 2016
Note: for better understanding, internet resources can also be used.
ADDITIONAL READINGS:
Note: Students are advised to contact with KFUEIT librarian for the provision of any paid e-book
or article (if required); however, a recommendation of the Instructor concerned shall be require
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