Linear Algebra: Systems of Linear Equations
N.B. Singh
This audiobook is narrated by a digital voice.
"Linear Algebra: Systems of Linear Equations" is an introductory textbook designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra. Through clear explanations, practical examples, and step-by-step guidance, this book demystifies the principles of systems of linear equations, equipping readers with essential skills to analyze and solve real-world problems using matrix operations, vector spaces, and foundational algebraic techniques. Ideal for students and self-learners alike, it aims to foster a deep understanding of linear algebra's relevance and applicability across various disciplines.
Duration - 3h 54m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. "Linear Algebra: Systems of Linear Equations" is an introductory textbook designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra. Through clear explanations, practical examples, and step-by-step guidance, this book demystifies the principles of systems of linear equations, equipping readers with essential skills to analyze and solve real-world problems using matrix operations, vector spaces, and foundational algebraic techniques. Ideal for students and self-learners alike, it aims to foster a deep understanding of linear algebra's relevance and applicability across various disciplines. Duration - 3h 54m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:01:37
Introduction to Systems of Linear Equations
Duration:00:00:51
Definition and Examples
Duration:00:02:48
Linear Systems in Real Life
Duration:00:04:35
Solutions and Solution Sets
Duration:00:04:27
Equivalent Systems
Duration:00:09:20
Geometric Interpretation
Duration:00:04:34
Gaussian Elimination
Duration:00:01:03
Row Operations
Duration:00:04:31
Row Echelon Form
Duration:00:03:36
Reduced Row Echelon Form
Duration:00:03:46
Pivots and Pivot Positions
Duration:00:03:35
Algorithmic Steps
Duration:00:03:41
Applications of Gaussian Elimination
Duration:00:04:28
Computational Considerations
Duration:00:06:01
Matrix Representation
Duration:00:01:04
Augmented Matrix
Duration:00:03:41
Matrix Notation
Duration:00:05:05
Coefficient Matrix
Duration:00:06:20
Vector of Variables
Duration:00:05:42
Matrix Equations
Duration:00:05:27
Row and Column Spaces
Duration:00:05:43
Rank and Nullity
Duration:00:05:34
Vector Spaces of Solutions
Duration:00:01:02
Solution Set of a System
Duration:00:05:46
Parametric Vector Form
Duration:00:04:51
Dimension of Solution Spaces
Duration:00:04:59
Fundamental Subspaces
Duration:00:02:45
Spanning and Basis of Solution Spaces
Duration:00:03:42
Linear Independence in Solution Spaces
Duration:00:08:56
Matrix Inverses
Duration:00:01:03
Definition and Existence
Duration:00:04:26
Properties of Inverse Matrices
Duration:00:03:42
Finding Inverses
Duration:00:05:42
Using Inverses to Solve Systems
Duration:00:06:06
Inverse of a 2x2 Matrix
Duration:00:05:27
Computational Aspects
Duration:00:06:34
Applications of Matrix Inverses
Duration:00:07:12
LU Decomposition
Duration:00:01:05
Definition and Factorization
Duration:00:06:30
LU Factorization Algorithm
Duration:00:06:11
Pivoting Strategies
Duration:00:03:25
Applications of LU Decomposition
Duration:00:04:17
Computational Efficiency
Duration:00:04:17
Relation to Gaussian Elimination
Duration:00:03:18
Variants and Extensions
Duration:00:03:20
Applications of Systems of Linear Equations
Duration:00:01:01
Applications in Engineering
Duration:00:04:18
Applications in Economics
Duration:00:04:32
Applications in Physics
Duration:00:04:49
Applications in Computer Science
Duration:00:04:33
Applications in Optimization
Duration:00:04:15
Applications in Data Analysis
Duration:00:04:22
Future Directions and Open Problems
Duration:00:04:15