M1 with Pre-requisites

Vector Algebra for Matrix Multiplication

2 Topics

Dot and Cross Product – Part 1

Dot and Cross Product – Part 2

Graphical Perspection of a Determinant – Part 1

1 Topic

Perspective – 1

Graphical Perspection of a Determinant – Part 2

1 Topic

Perspective – 2

Inverse of a Matrix

5 Topics

Introduction – 2X2 – Matrix

Example – 2X2 – Matrix

General procedure and Incidental facts – 3X3 Matrix

Matrix-Vector Multiplication

5 Topics

Introduction – Perspective 1 – Linear Algebra

Introduction – Perspective 2 – Linear Algebra

Matrix-Matrix Multiplication – Part 1

4 Topics

Introduction – Perspective – Linear Algebra

Introduction – Alternate Method

Matrix-Matrix Multiplication – Part 2

1 Topic

Matrix-Matrix Multiplication – Part 3

2 Topics

1 Quiz

Prerequisites for Module-5: Linear Algebra | Quiz Questions

Module-5: Linear Algebra

Introduction to Rank of a Matrix – Part 1

2 Topics

Concept of Rank – (Basis definition of Rank)

Concept of Rank – (Linearly dependent and independent vectors)

Introduction to Rank of a Matrix – Part 2

1 Topic

Concept of Rank – (Graphical Understanding – 1)

Rank of a Matrix

15 Topics

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)

Introduction to Simultaneous equations

3 Topics

Simultaneous Equations – (Introduction)

Simultaneous Equations – (Classifications)

Simultaneous Equations – (Introductory Example)

Simultaneous equations

18 Topics

Solutions to Simultaneous Equations – (Possibility 1 – Unique Solution)

Solutions to Simultaneous Equations – (Possibility 2 – No Solution)

Solutions to Simultaneous Equations – (Possibility 3 – Infinite Solution)

Solutions to Simultaneous Equations – (Example – General case)

Solutions to Simultaneous Equations – (Understanding – 3 Variable situation)

Solutions to Simultaneous Equations – (Checking for Consistency of solution – 3 Variable situation)

Solutions to Simultaneous Equations – (Graphical Understanding of Consistency – 3 Variable)

Solutions to Simultaneous Equations – Problems: (Problem 1)

Solutions to Simultaneous Equations – Problems: (Problem 2)

Solutions to Simultaneous Equations – Problems: (Problem 3)

Gauss – Jordan Method – Problems: (Problem 1)

Gauss – Jordan Method – Problems: (Problem 2)

Gauss – Jordan Method – Problems: (Problem 3)

Gauss – Elimination Method – Problems: (Problem 1)

Gauss – Elimination Method – Problems: (Problem 2 (2 approaches))

Gauss-Seidel method – (Conceptual Understanding)

Gauss-Seidel method – Problems: (Problem 1)

Gauss-Seidel method – Problems: (Problem 2)

Introduction to Eigenvalues and Eigenvectors

3 Topics

Graphical Understanding of Eigenvalues and Eigenvectors

Understanding Eigen values – 2×2 matrix

Eigenvalues and Eigenvectors – Part 1

4 Topics

Eigen values – Observations

Eigen values – Example

Deriving Eigen vectors – 2×2 matrix

Eigen vectors – Observations

Eigenvalues and Eigenvectors – Part 2

1 Topic

Deriving Eigen value and vectors – 3×3 matrix

Eigenvalues and Eigenvectors – Part 3

4 Topics

Rayleigh’s Power Method – (Conceptual Understanding)

Rayleigh’s Power Method – Problems: (Problem 1)

Rayleigh’s Power Method – Problems: (Problem 2)

Rayleigh’s Power Method – (Conceptual Understanding of Rate of Convergence)

13 Topics

Concept of Rank: (Formula & Procedure)

Concept of Rank: (Important Observations)

Concept of Rank: (Obvious and Unobvious Facts)

Concept of Rank: (Engineering Facts/Mapping)

Simultaneous Equations: (Formula & Procedure)

Simultaneous Equation Methods: (Formula & Procedure)

Gauss-Seidel Method: (Formula & Procedure)

Simultaneous Equations: (Obvious and Unobvious Facts)

Simultaneous Equations: (Engineering Facts/Mapping)

Eigen values and vectors: (Formula & Procedure)

Rayleigh Power Method: (Formula & Procedure)

Eigen values and vectors: (Obvious and Unobvious Facts)

Eigen values and vectors: (Engineering Facts/Mapping)

1 Quiz

Module-5: Linear Algebra | Quiz Questions

5 of 6

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Introduction

M1 with Pre-requisites Introduction to Eigenvalues and Eigenvectors Introduction

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