Introduction to system of linear equations

Matrix form of system of Linear Equations

Consistent and inconsistent systems

Gauss-Jorden Method

Homogeneous system of equations

Gaussian Elimination method

Introduction to vector in plane

Vector in RPn

Vector form of straight line

Linear Combinations

Geometrical interpretation of solution of Homogeneous and Non-homogeneous equation

Traffic Flow Problem

Electric circuit Problem

Economic Model

Introduction to linear transformations

Matrix transformations

Domain and range of linear transformations

Geometric interpretation of linear transformations

Matrix of linear transformations

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

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

Introduction to Eigen value and Eigen vectors

Computing the Eigen values

Properties of Eigen values

Diagonalization

Applications of Eigen values