DEPARTMENT OF COMPUTER ENGINEERING
The University of Lahore
1 - KM Defence Road, Lahore
Course Hand Book
Course Title
Linear Algebra
2
3
4
5
6
7
8
9
Course Code
Credit Hours
Pre Requisite
Lecture days
Contact Hours (Theory)
Contact Hours (Lab)
Section
Instructor
MA2320
10
11
12
13
14
Office
Telephone/Email
Website
Visiting Hours
Course Introduction
CE03
3
NIL
Thursday , Friday
3 hours/ week
A
Engr. Obaid Ur Rehman
Tuesday (11:00-14:00), Wednesday (13:30-16:30)
In this course, Expertise of the students will be developed in the field of Linear Algebra and analysis of
vector spaces through matrix operations. The main topics that will be covered in this subject are, Vector
algebra, Matrix algebra, Properties of Matrices and its Determinants, Vector Spaces, Solution of linear
equations, Orthogonality principle, Eigen-analysis, and the application of Matrices in Engineering.
15
Learning Objectives
1.
CLO:1. Acquire knowledge related to basic concepts, and understanding of vectors and Matrices.
2.
CLO:2. Understanding Vector spaces and subspaces.
3.
CLO:3. Understanding the Solution of linear equations.
4.
CLO:4. Understanding the basics of Eigen analysis.
5.
CLO:5. Develop rational thinking patterns in terms of problem solving skills through logical reasoning.
16
Course Contents
Vectors, Vector Spaces, Matrices & Determinants, Cofactor and Inverse, Rank, Linear Independence,
Solution of System of Linear systems, Positive Definite matrix, Linear Transformations, Operations of
Matrices, Inner products, Orthogonality and least squares, Eigenvalue and Eigen Vectors, Applications to
System of Equations and to geometry, and Singular Value Decomposition.
17
Lecture Break Up
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
19
Topic of Lecture
Vectors and Linear Combinations
Linear Dependence and Independence
Assignment 1
Length and Dot Products
Quiz 1
Vectors and Linear Equations
Elimination using Matrices
Rules for Matrix Operations
Inverse Matrices
Transpose and Permutations
Assignment 2
Spaces of Vectors
The Nullspace of A: Solving Ax= 0
Quiz 2
The Rank and the Row Reduced Form
The Complete Solution to Ax = b
Independence, Basis and Dimension
Dimensions of the Four Subspaces
Orthogonality of the Four Subspaces
Orthogonal Bases and Gram-Schmidt
The Properties of Determinants
Permutations and Cofactors
Cramer’s Rule, Inverse, and Volumes
Assignment 3
Introduction to Eigenvalues
Diagonalizing a Matrix
Applications to Differential Equations
Quiz 3
Symmetric Matrices
Positive Definite Matrices
Similar Matrices
Singular Value Decomposition (SVD)
The idea of a Linear Transformation
The matrix of a Linear Transformation
Assignment 4
Change of Basis
Diagonalization and the Pseudoinverse
Quiz 4
Matrices in Engineering
Graphs and Networks
Course Assessment Policy and Grading
The total hours should equal the learning hours for the module and is made up of the teaching
contact hours as well as the students' private study hours.
THEORY (100%)
Type
Hours
Teaching Contact Hours
Instructors Office Hours
3 hours/ week
5 hours/ week
Percentage Break Up
Theory (Total Weightage = 100 %)
Exam
Quantity
Weightage
1.
2.
3.
4.
1
1
4
4
30
50
10
10
MidTerm
Final Exam
Quiz
Assignments
20.
Text Book/s
Gilbert Strang, " Introduction to Linear Algebra ", WellesleyCambridge Press, (Latest Edition)
21.
Reference Books
Howard Anton / Chris Rorres, “Elementary Linear Algebra” 10 th
Edition.
22.
Plagiarism Policy
Plagiarism involves the unacknowledged use of someone else’s work, usually in coursework, and passing it
off as if it were one’s own. Many students who submit apparently plagiarised work probably do so
inadvertently without realising it because of poorly developed study skills, including note taking, referencing
and citations; this is poor academic practice rather than malpractice. Study skills education within
programmes of study should minimise the number of students submitting poorly referenced work. However,
some students plagiarise deliberately, with the intent to deceive. This intentional malpractice is a conscious,
pre-mediated form of cheating and is regarded as a particularly serious breach of the core values of
academic integrity. The Computer Engineering Programme has zero tolerance for intentional plagiarism.
23.
Attendance Policy
Every student must attend 80% of the lectures/seminars delivered in each course and 80% of the
practical/laboratory work prescribed for the respective courses. The students having short of required
percentage of attendance of lectures/seminars/practical/laboratory work, etc., shall not be allowed to appear
in the terminal examination of this course and shall be treated as having failed this course.
24.
Project / Report / Simulation
25.
Field Trips/Case Studies/Seminars/Workshop
26.
Mapping of Course Learning Objective to Program Learning Objective
CLOs/PLOs
CLO:1
PLO:1 (Knowledge Base)
√
PLO:2 (Application)
√
CLO:2
CLO:3
CLO:4
CLO:5
√
PLO:3 (Designing Skills)
√
PLO:4 (Problem Solving)
√
PLO:5 (Analysis and Critical Thinking)
√
√
√
√
√
√
PLO:6 (Industrial Tools)
PLO:7 (Engineering Management Skills)
PLO:8 (Professionalism and Ethics)
PLO:9 (Professional Development and Selflearning)
√
√
PLO:10 (Team Work)
√
√
PLO:11 (Communication Skills)
√
√
27.
Mapping of CLOs to Assessment Modules
Assessment Modules
CLO1
CLO2
CLO3
CLO4
CLO5
CLOs/Assessment Modules
CLO:1
CLO:2
CLO:3
CLO:4
CLO:5
Assignments
√
√
√
√
√
Quizzes
√
√
Midterm Exam
√
√
Final Exam
√
√
Project
√
√
√
√
√