Linear Algebra

Calculus and Analytical Geometry (MT-1013)

Linear Algebra And Its Applications,  4^th  Edition By David C. Lay

Howard Antone, Chris Rorres, Elementary Linear Algebra And Its Applications

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)

CLO:1. Define how to calculate and measure Voltage, Current and Resistance, connectivity etc. using digital multimeter and express knowledge of handling Power Trainer, Function Generator and Oscilloscope (Level: P1)

CLO:2. Use the knowledge acquired in lab and course to construct and investigate basic electronic circuit like dc power supply to harvest knowledge of all its intermediate stages  (Level: C6)

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