I am taking a Linear algebra course from Coursera. I have completed the following topic from there, and I will be sharing some concepts:
Systems of linear equations
Singular and non-singular matrices
Determinants
The rank of a matrix
Row reduction
Null space
System of sentences:
System-01
The dog is black
The cat is orange
The bird is red
System-02
The dog is black
The dog is black
The bird is red
System-03
The dog is black
The dog is black
The dog is black
System-04
The dog is black
The dog is white
The dog is red
System-01 is a complete system. System-02 is a redundant system. System-03 is a redundant system. System-04 is a contradictory system.
A complete system is a non-singular system. A redundant system is a singular system. A contradictory system is a singular system.
Summary:
Complete = non-singular; Redundant = Singular; Contradictory = Singular;
System of Linear Equations:
Unique solution: Complete: Non-singular
Infinite solutions : Redundant: Singular
No solution: Contradictory: Singular
Linear Equation: A simple equation not having any complex sign or notation.
Task: Learn how to plot a graph of a system of linear equations
If two lines touch each other at one point: Unique solution: Complete: Non-singular;
If two lines lie in the same location in a graph: Infinite solutions: Redundant: Singular;
If two lines never touch each other in a graph: Any solutions: Contradictory: singular;
A Geometric notion(concept) of singularity
The constant after two variables which lies after equal sign doesn't contribute anything to the equation. It means if we make it zero, it doesn't affect the graph.
Singular Vs Non-singular matrices
Linear dependence and independence
If no equation is a multiple of the other one= Rows are linearly independent
If one equation is a multiple of the first one= Rows are linearly dependent
The determinant
If the determinant of a matrix is 0 = Singular matrix or equation
If the determinant of a matrix is 1 = Non-singular matrix or question
TIPS: non-zero determinant= non-singular matrix
To be continue....