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# Matrix Algebra and Rank

149.00

Validity: 45 days | Duration: 6hrs 43mins

Boost your engineering skills with Matrix Algebra and Rank. A compact course for UG students in India. Reinforce learning with hands-on examples

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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