Course Outline Format
BS (IE)
Program
3
Credit Hours
15 weeks
Duration
Linear Algebra (IE-A)
Prerequisites
Dr. Muhammad Javaid
Resource Person
Tuesday: 9:00am-12:30pm
Thursday: 9:00am-12:30pm
Counseling Timing
Friday: 9:00am-12:30pm
03006547620
Contact
Chairman/Director Programme signature………………. Dean’s signature…………
Date………………………………….
Learning Objective
An introduction to the algebra and geometry of vector spaces and matrices, this
course stresses important mathematical concepts and tools used in advanced
Mathematics, Computer Science, Physics and Economics. A systematic method of
solving systems of linear equations is the underlying theme and applications of
the theory will be emphasized. Topics of exploration include Gaussian elimination,
determinants, linear transformations, equations of line and plane. In general, this
course directly contributes to all theobjectives of the HEC Software Engineering
Curriculum 2014. However, in particularly at the end of the course, students
should be able to;
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Express a system of equations in the form of matrices.
Apply different techniques for the solution of the system of equations.
Familiar with vectors in two and three dimensions and their properties.
Understand the concept of a vector space and its various models.
Know the concept of linear transformation and its application
Learning Methodology
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Discussion of the elementary knowledge in class.
A Comprehensive presentation of the definitions in class.
Explanation with examples in class.
Practice questions in class.
Assignments as home work.
Office Hours for individual problems of the students.
Quizzes, midterm, and final term examsfor evaluation.
Grade Evaluation Criteria
Following is the criteria for the distribution of marks to evaluate final grade in a
semester.
Marks Evaluation
 Qizzes+Assignments+
Attendance & Class Participation
 Mid Term
Marks in percentage
25%
25%
 Presentations0%
 Term Project0%
 Final exam50%
Total
100%
Recommended Text Books
 Anton, Howard, Elementary linear Algebra, 10th Edition. Wiley publishing,
2005.
Reference Books
 Gilbert Strang, Linear Algebra and its Applications, Fourth Edition
 David C. Lay, Linear Algebra and its Applications, Latest Edition
 James M. Ortega, Matrix Theory-A Second Course,
Calendar of Course contents to be covered during semester
week
1
Activity
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Introduction to matrices, Algebra of matrices.
Multiplication of matrices
2
3
Reference
TB* Chapter 1
TB Chapter 1
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Elementary row operations
Echelon and reduced Echelon form of matrix
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Inverse of a matrix using elementary row
operations
Introduction to system of linear equations
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TB Chapter 1
4
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Gauss elimination and Gauss Jordan method for solution
of non homogenous systems
Consistency criterion for solution of linear equations
TB Chapter 1
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Homogenous systems of equations, trivial and non‐trivial
solutions
Evaluating determinants using cofactors and Minors
TB Chapter 1
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Properties of determinants
Application of determinants to system of linear equations
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Vectors and their algebra
Inner products, projection and orthogonality of vectors
8
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Gram‐Schmidt process
TB Chapter 3
9
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Least Square Method
TB Chapter 3
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5
6
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TB Chapter 2
7
TB Chapter 3
10
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Vector spaces
Sub spaces
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Linear combination
Linear independence and dependence of vectors
12
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Spanning sets and generators, null space
Basis and dimensions
13
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Linear transformation
Matrix representations of linear transformations
Eigen Values and Eigen vectors of matrices
Problems relating to Eigen values and vectors.
11
TB Chapter 4
TB Chapter 4
TB Chapter 4
TB Chapter 5
14
15
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Positive definite matrix
Singular Value Decomposition
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Application of Linear Systems to Geometry
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Application of linear systems (Electric circuit and Network
problems)
TB Chapter 6
TB Chapter 6