LINEAR ALGEBRA

UNIT-I

Systems of Linear Equations and Matrices

06 Hrs

1.1 Row echelon form of a matrix, reduced row echelon form of a matrix.

1.2 Definition of rank of a matrix using row echelon or row reduced echelon form.

1.3 System of linear equations- Introduction, matrix form of linear system, definition of row equivalent matrices.

1.4 Consistency of homogeneous and non-homogeneous system of linear equations using rank, condition for consistency

1.5 Solution of System of Equations: Gauss elimination and Gauss-Jordan elimination method, examples.

UNIT-II

Vector Spaces-I

06 Hrs

2.1 Definition and examples

2.2 Subspaces

2.3 Linear Dependence and Independence (Statement and examples only)

2.4 Basis of vector space

UNIT-III

Vector Spaces-II

06 Hrs

3.1 Dimension of a vector space

3.2 Row Space, Column Space, and Null Space of a matrix

3.3 Definition: Rank and Nullity

UNIT-IV

Eigen Values and Eigen Vectors

06 Hrs

4.1 Eigen values

4.2 Eigen vectors

4.3 Diagonalization

UNIT-V

Linear Transformations

06 Hrs

5.1 Definition and Examples, Properties, Equality

5.2 Kernel and range of a linear Transformation

5.3 Rank-Nullity theorem (Statement only)

5.4 Matrix representation of Linear Transformation

UNIT-I

Systems of Linear Equations and Matrices

06 Hrs

1.1 Row echelon form of a matrix, reduced row echelon form of a matrix.

1.2 Definition of rank of a matrix using row echelon or row reduced echelon form.

1.3 System of linear equations- Introduction, matrix form of linear system, definition of row equivalent matrices.

1.4 Consistency of homogeneous and non-homogeneous system of linear equations using rank, condition for consistency

1.5 Solution of System of Equations: Gauss elimination and Gauss-Jordan elimination method, examples.

UNIT-II

Vector Spaces-I

06 Hrs

2.1 Definition and examples

2.2 Subspaces

2.3 Linear Dependence and Independence (Statement and examples only)

2.4 Basis of vector space

UNIT-III

Vector Spaces-II

06 Hrs

3.1 Dimension of a vector space

3.2 Row Space, Column Space, and Null Space of a matrix

3.3 Definition: Rank and Nullity

UNIT-IV

Eigen Values and Eigen Vectors

06 Hrs

4.1 Eigen values

4.2 Eigen vectors

4.3 Diagonalization

UNIT-V

Linear Transformations

06 Hrs

5.1 Definition and Examples, Properties, Equality

5.2 Kernel and range of a linear Transformation

5.3 Rank-Nullity theorem (Statement only)

5.4 Matrix representation of Linear Transformation