This module covers both algebraic and graphical approaches to evaluating the characteristics of matrices. A detailed account on row/column reductions to Echelon form and hence Rank of a matrix and its graphical understanding. LU decomposition is discussed as a special case of matrix-matrix multiplication. Significant number of model questions paper problems have been solved to give a comprehensive understanding of the examinerâ€™s perspective.

Salient features of this module are:

- Pre-requisites to Fundamental Matrix Theory
- Graphical visualization
- Concept testing
- Unravelling examiners mind
- Model question paper

**Course Contents:Â **

**Pre-requisites to Matrix Algebra and Rank**

**Types of Matrices**- Types of Matrices – Part 1
- Types of Matrices – Part 2
- Types of Matrices – Part 3

**Understanding Determinant**- Determinant of a 3×3 matrix
- Determinant of a 4×4 matrix

**Vector Algebra for Matrix Multiplication**- Dot and Cross Product – Part 1
- Dot and Cross Product – Part 2

**Graphical Perspection of a Determinant**- Perspective – 1
- Perspective – 2

**Inverse of a Matrixe**- Introduction – 2X2 – Matrix
- Example – 2X2 – Matrix
- General procedure and Incidental facts – 3X3 Matrix
- Observations
- Applications

**Matrix-Vector Multiplication**- Introduction – Perspective 1 – Linear Algebra
- Introduction – Perspective 2 – Linear Algebra
- Quiz 1
- Quiz 2
- Quiz 3

**Matrix-Matrix Multiplication**- Introduction – Perspective – Linear Algebra
- Introduction – Alternate Method
- Quiz 1
- Quiz 2
- Quiz 3
- Quiz 4
- Quiz 5

**Matrix algebra & Rank **

**Rank of a Matrix**- Concept of Rank – (Basis definition of Rank)
- Concept of Rank – (Linearly dependent and independent vectors)
- Concept of Rank – (Graphical Understanding – 1)
- Linear Algebra – (Rank – Graphical Understanding – 2)
- Linear Algebra – (Rank – Linear Algebra/Transformation Perspective)
- Linear Algebra – (Final observations/conclusions)
- Rank/Row and Column Reduction – Problems: (problem 1 – Row reduction)
- Rank/Row and Column Reduction – Problems: (problem 2 – Column reduction)
- Rank/Row and Column Reduction – (Understanding the Echelon and observations)
- Rank/Row and Column Reduction – (Understanding the Echelon and Normal form of a matrix)
- Rank/Echelon form – Problems: (Problem 1)
- Rank/Echelon form – Problems: (Problem 2)
- Rank/Echelon form – Problems: (Problem 3)
- Rank/Echelon form – Problems: (Problem 4)
- Rank/Echelon form – Problems: (Problem 5)
- Rank/Echelon form – Problems: (Problem 6)
- Rank/Echelon form – Problems: (Problem 7)
- Rank/Echelon form – Problems: (Problem 8)

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