Contents

1. Introduction

1. Introduction

2. Matrix Operations

3. The Inverse of a Matrix

4. Characterisation of Invertible Matrices

2. Linear Equations in Linear Algebra-I 

1. Introduction

2. System of Linear Equations  

3. Row Reduction and Echelon Forms  

4. Vector Equations 

5. The Matrix Equation Ax = b

6. Solution Sets of Linear Systems

3. Linear Equations in Linear Algebra–II

1. Introduction

2. Partitioned Matrices   

3. Matrix Factorization (LU-Decomposition Method)   

4. Linear Independence    

5. Introduction to Linear Transformation  

6. The Matrix of a Linear Transformation  

7. Subspaces of Rⁿ   

8.   Dimension and Rank

4. Determinants

1. Introduction

2. Introduction to Determinants

3. Properties of Determinants  

4. Cramer's Rule, Volume and Linear Transformations