This site contains a Geogebra applet that demonstrates the effect of linear transformation in R2 on a graphical image. It also finds the determinant, trace, norm, eigenvalues and eigenvectors of the underlying matrix.
It shows the 2x2 matrix and the image of its two basis vectors.
Type of Material:
Simulation
Animation
Recommended Uses:
Homework, in-class examples, computer lab sessions, individual learning, or group exploration in mathematics-related courses.
Technical Requirements:
Any browser and it uses Geogebra
Identify Major Learning Goals:
The primary purpose of this GeoGebra resource is to provide an interactive platform for understanding the properties, applications, and transformations of 2x2 matrices. This tool is designed to help learners build a better intuitive and visual understanding of the properties of linear transformations and their underlying matrices and the linear algebra concepts through hands-on exploration.
Target Student Population:
Students taking Linear Algebra or related upper math courses.
Also graduate school
Prerequisite Knowledge or Skills:
Students should have a basic understanding of linear algebra (e.g., matrix notation, operations, and properties) and familiarity with vector representation in 2D space is helpful but not mandatory.
Content Quality
Rating:
Strengths:
This tool is designed to help students visualize linear transformations acting on two-dimensional real space. Demonstrated effects are closely related to a 2x2 matrix that represents this linear transformation. The applet calculates and shows the matrix, its determinant and trace as well as its eigenvalues and eigenvectors.
The site’s strength lies in its ability for its interactive visualizations, hands-on learning, It supports multiple learning styles and promotes critical thinking.
Concerns:
The site would benefit from having a paragraph or two (or a link to) with explanations of main concepts. A user could use a guidance explaining the results.
It has limited depth for advanced topics. While effective for basic and intermediate exploration, This site may lack the capability to fully support advanced linear algebra concepts (e.g., complex eigenvalues or higher-dimensional matrices).
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The applet is highly effective as it utilizes a visual approach to demonstrate some basic Linear Algebra concepts. As a support and demonstration tool, instructors can use the site to illustrate textbook examples and homework assignments. Students could benefit from visiting the site and spending 20-30 minutes checking their homework or working through a planned worksheet.
The tool is highly effective for student learning due to its interactive, visual approach that helps build intuition about integral approximations. It has the ability to enhance conceptual understanding and links theoretical calculations to geometric interpretations, reinforcing the connection between algebra and geometry.
Concerns:
Without proper guidance, students may not be able to interpret visual outputs.
It has the potential for misinterpretation. Without proper guidance, students may misinterpret visual outputs (e.g., not understanding why a determinant of zero indicates a non-invertible matrix).
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This is a very straightforward applet to use. The average user should be able to run it immediately. The zoom feature is very helpful.
It has user-friendly navigation. Navigating through the software is straightforward, with drag-and-drop capabilities and interactive sliders enhancing usability
Concerns:
The presence of adds in the bottom of the screen is a bit annoying.
Users may occasionally find the interface overwhelming due to the variety of available tools. In addition, it lacks integrated examples or tutorials: GeoGebra may not provide built-in examples or step-by-step guides to help users explore concepts like how a determinant relates to area scaling or how eigenvalues affect transformations.
Creative Commons:
Search by ISBN?
It looks like you have entered an ISBN number. Would you like to search using what you have
entered as an ISBN number?
Searching for Members?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.
Searching for Members?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.
