Academics Links
Linear Algebra (MTC1033)
Prerequisite(s)
Calculus and Analytical Geometry (MT1013)
Recommended Book(s)
Linear Algebra And Its Applications, 4^{th} Edition By David C. Lay
Reference Book(s)
Howard Antone, Chris Rorres, Elementary Linear Algebra And Its Applications
Course Objectives
The principle aim of this course is to understand several important concepts in linear algebra, including systems of linear equations and their solutions; matrices and their properties; determinants and their properties; vector spaces; linear independence of vectors; subspaces, bases, and dimension of vector spaces; inner product spaces; linear transformations; and Eigen values and eigenvectors. These concepts are then implemented in a MATLAB to give them a broader view of the course.
Course Learning Outcomes (CLO)
CLO:1. Illustrate how to solve a system of linear equations that appears in circuit analysis, electromagnetic fields and waves, antenna theory, microwaves, etc. (Level: C2)
CLO:2. Interpret the vector equations and linear transformations which are used in image processing, Control theory, etc. (Level: C3)
CLO:3. Apply the basic knowledge of vector spaces, Eigen value and Eigen vectors which are help full in image processing, control theory, etc. (Level: C3)
CLO:4. Develop a solid understanding of the course by implementing the key concepts in MATLAB environment. (Level: P2)
Course Contents
System of Linear Equations and Matrices
Introduction to system of linear equations
Matrix form of system of Linear Equations
Gaussian Elimination method
GaussJorden Method
Consistent and inconsistent systems
Homogeneous system of equations
Vector Equations
Introduction to vector in plane
Vector in RP^{n}
Vector form of straight line
Linear Combinations
Geometrical interpretation of solution of Homogeneous and Nonhomogeneous equations
Applications of Linear Systems
Traffic Flow Problem
Electric circuit Problem
Economic Model
Linear transformations
Introduction to linear transformations
Matrix transformations
Domain and range of linear transformations
Geometric interpretation of linear transformations
Matrix of linear transformations
Inverse of a matrix
Definition of inverse of a matrix
Algorithm to find the inverse of matrices
LU factorization
Determinants
Introduction to determinants
Geometric meaning of determinants
Properties of determinants
Crammer Rule
Cofactor method for finding the inverse of a matrix
Vector Spaces
Definition of vector spaces
Subspaces
Spanning set
Null Spaces and column spaces of linear transformation
Linearly Independent sets and basis
Bases for Null space and Kernal space
Dimension of a vector space
Eigen Values and Eigen vectors
Introduction to eigen value and eigen vectors
Computing the eigen values
Properties of eigen values
Diagonalization
Applications of eigen values
Mapping of CLOs to Program Learning Outcomes
CLOs/PLOs 
CLO:1 
CLO:2 
CLO:3 
CLO:4 
PLO:1 (Engineering Knowledge) 
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√ 
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PLO:2 (Problem Analysis) 




PLO:3 (Design and Development of Solutions) 




PLO:4 (Investigation) 




PLO:5 (Modern Tool Usage) 



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PLO:6 (The Engineer and Society) 




PLO:7 (Environment and Sustainability) 




PLO:8 (Ethics) 




PLO:9 (Individual and Team Work) 




PLO:10 (Communication) 




PLO:11 (Project Management) 




PLO:12 (Life Long Learning) 



