Matrix Algebra and Rank

Prerequisites for Matrix algebra & Rank

Types of Matrices

3 Topics

Types of Matrices – Part 1

Types of Matrices – Part 2

Types of Matrices – Part 3

Understanding Determinant

2 Topics

Determinent of a 3X3 matrix

Determinent of a 4X4 matrix

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

Matrix algebra & Rank

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)

Previous Lesson

Perspective – 1

Matrix Algebra and Rank Graphical Perspection of a Determinant – Part 1 Perspective – 1

Previous Lesson

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