Transforming Linear Algebra Education with GeoGebra

James D. Factor, Aug 10, 2017

[i][/i]This Linear Algebra GeoGebra Book was developed under the NSF TUES Grant Award ID: 1141045 [i]Transforming Linear Algebra Education with GeoGebra Applets [/i]

Table of Contents

  1. Notes:
    1. Copy of Using/Interacting with Applets, Activities, and Feedback
  2. Vectors
    1. Meaning of a Vector
    2. Vector Properties
    3. * Associativity - Property 2 - 3D
    4. Unit Vectors and Normalization
    5. Linear Combinations
    6. Change of Basis
    7. Lines & Planes: Vector Forms
    8. Cross Product (Not Uploaded)
    9. Line: Normal Form
    10. Plane: Normal Form
    11. Vector Projection
    12. Gram-Schmidt Process
    13. STEM - Chemistry: Molecule
  3. Linear Systems
    1. Matrix View (Not Uploaded)
    2. Row View(Not Uploaded)
    3. Column View(Not Uploaded)
    4. Solving Systems: Direct Methods & Echelon Forms(Not Uploaded)
    5. Gauss-Jordan Elimination
  4. Matrices
    1. Matrix Basics(Not Uploaded)
    2. Inverse Matrix(Not Uploaded)
    3. Linear Transformations - Part 1
    4. Linear Transformations - Part 2
  5. Vector Spaces
    1. Vector Space Definition
    2. * Associativity - 3D
    3. Least Squares Approximation
    4. Spanning Spaces(Not Uploaded)
    5. Eigenvectors and EigenValues(Not Uploaded)

1.

Notes:

  • 1. Copy of Using/Interacting with Applets, Activities, and Feedback

1.1.

Copy of Using/Interacting with Applets, Activities, and Feedback

Notes: Using Video, Applets, Activity
– James D. Factor

2.

Vectors

  • 1. Meaning of a Vector
  • 2. Vector Properties
  • 3. * Associativity - Property 2 - 3D
  • 4. Unit Vectors and Normalization
  • 5. Linear Combinations
  • 6. Change of Basis
  • 7. Lines & Planes: Vector Forms
  • 8. Cross Product (Not Uploaded)
  • 9. Line: Normal Form
  • 10. Plane: Normal Form
  • 11. Vector Projection
  • 12. Gram-Schmidt Process
  • 13. STEM - Chemistry: Molecule

2.1.

Meaning of a Vector

Video - Meaning of a Vector versus a Point
Applet - Meaning of a Vector versus a Point
Activity - Meaning of a Vector versus a Point
– James D. Factor

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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3.

Linear Systems

Linear System Views Solving Linear Systems Linear Transformations - Part 1 Linear Transformations - Part 2

  • 1. Matrix View (Not Uploaded)
  • 2. Row View(Not Uploaded)
  • 3. Column View(Not Uploaded)
  • 4. Solving Systems: Direct Methods & Echelon Forms(Not Uploaded)
  • 5. Gauss-Jordan Elimination

3.1.

Matrix View (Not Uploaded)

– James D. Factor

3.2.

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3.3.

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3.4.

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3.5.

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4.

Matrices

Matrix Basics Inverse Matrix LT Matrix

  • 1. Matrix Basics(Not Uploaded)
  • 2. Inverse Matrix(Not Uploaded)
  • 3. Linear Transformations - Part 1
  • 4. Linear Transformations - Part 2

4.1.

Matrix Basics(Not Uploaded)

– James D. Factor

4.2.

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4.3.

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4.4.

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5.

Vector Spaces

Vector Space Basics Least Squares Approximation Spanning Spaces Eigen Vectors& Values

  • 1. Vector Space Definition
  • 2. * Associativity - 3D
  • 3. Least Squares Approximation
  • 4. Spanning Spaces(Not Uploaded)
  • 5. Eigenvectors and EigenValues(Not Uploaded)

5.1.

Vector Space Definition

Video - Vector Space Definition
Applet - Vector Space Definition
Vector Space Definition (Properties ) - Activity
– James D. Factor

5.2.

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5.3.

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5.4.

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5.5.

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Information