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
    • 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
      9. 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