# Linear Algebra (MTC1033)

##### Pre-requisite(s)

Calculus and Analytical Geometry (MT-1013)

##### Recommended Book(s)

Linear Algebra And Its Applications,  4th  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

Gauss-Jorden Method

Consistent and inconsistent systems

Homogeneous system of equations

##### Vector Equations

Introduction to vector in plane

Vector in RPn

Vector form of straight line

Linear Combinations

Geometrical interpretation of solution of Homogeneous and Non-homogeneous 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) √ √ √ PLO:2 (Problem Analysis) PLO:3 (Design and Development of Solutions) PLO:4 (Investigation) PLO:5 (Modern Tool Usage) √ 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)