## 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.Interpret the vector equations and linear transformations. (Level: C1)
CLO: 2.Illustrate how to solve a system of linear equations that appears different engineering applications. (Level: C2)
CLO: 3. CLO:3. Apply the basic knowledge of vector spaces, Eigen value and Eigen vectors. (Level: C3)

## COURSE CONTENTS

1. System of Linear Equations and Matrices-Four Lectures
• 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
2. Vector Equations-Four Lectures
• Introduction to vector in plane
• Vector in Rn
• Vector form of straight line
• Linear Combinations
• Geometrical interpretation of solution of Homogeneous and Non-homogeneous equations
3. Applications of Linear Systems-Two Lectures
• Traffic Flow Problem
• Electric circuit Problem
• Economic Model
4. Linear transformations-Four Lectures
• Introduction to linear transformations
• Matrix transformations
• Domain and range of linear transformations
• Geometric interpretation of linear transformations
• Matrix of linear transformations
5. Inverse of a matrix-Four Lectures
• Definition of inverse of a matrix
• Algorithm to find the inverse of matrices
• LU factorization
6. Introduction to determinants
• Geometric meaning of determinants
• Properties of determinants
• Crammer Rule
• Cofactor method for finding the inverse of a matrix
7. Vector Spaces-Three Lectures
• 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
8. Eigen Values and Eigen vectors-Three Lectures
• Introduction to eigen value and eigen vectors
• Computing the eigen values
• Properties of eigen values
• Diagonalization
• Applications of eigen values