Linear Algebra with GeoGebra

Transforming Linear Algebra Education with GeoGebra Applets

James D. Factor (PI); Susan Pustejovsky (Co-PI), Alverno College‌                   

           

 

       NSF TUES Grant Award ID: 1141045

 

Transforming Linear Algebra with GeoGebra 

https://www.geogebra.org/m/XnfUWvvp

Objectives

• Promote a deeper understanding of linear algebra and its applications
• Actively engage the student in exploring concepts
• Help the student visualize linear algebra operations
• Foster deeper understanding of algebraic, geometric, and numeric perspectives of linear algebra ‌

GeoGebra Applets

• Applet packages for 12 areas of linear algebra
• 2D and 3D interactive animation applets
• Instructional support for each linear algebra package

 ‌

Note: The material below consists of old draft versions.                         This section will be updated.  

Applet Topics

• Exploring basic operations of vectors in R² and R³
  •  
  • S1L1 - Vector Package - Draft.ggb
• Exploring basic geometric operations of vectors in R² and R³
  
  • 2.1.2D Dot Product.ggb
  • 2.1.2D Dot Product.html
• Illustrating geometric approaches to the proof of key properties
• Geometric illustration of linear combinations and coordinates
  • 4.1.2D Coordinate Grid.ggb
  • 4.1.2D Coordinate Grid.html
• Linear systems of equations
  • 5.1.3D Planes Intersect.ggb
• Spanning spaces in R² and R³
  
• Spanning subspaces in R² and R³
  
  • 7.1.3D BasisForSubspace.ggb
• Row, column, and null subspaces
• Linear transformations in R² and R³
  
• Geometric illustration of eigenvalues, eigenvectors, and eigenspaces
• Geometric application of determinants
• Orthogonal and orthonormal basis