I am taking a Linear algebra course from Coursera. I have completed the following topic from there, and I will be sharing some concepts:

1. Systems of linear equations

2. Singular and non-singular matrices

3. Determinants

4. The rank of a matrix

5. Row reduction

6. Null space

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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.

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A complete system is a non-singular system. A redundant system is a singular system. A contradictory system is a singular system.

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Summary:

Complete = non-singular; Redundant = Singular; Contradictory = Singular;

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System of Linear Equations:

Unique solution: Complete: Non-singular

Infinite solutions : Redundant: Singular

No solution: Contradictory: Singular

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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;

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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.

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Singular Vs Non-singular matrices

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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

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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

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To be continue....