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Journal of Online Mathematics and its Applications
Tool Building: Web-based Linear Algebra Modules
Eigenizer Tool and Sample Activity
Working with Eigenizer, similar to Transformer2D, involves coordinated actions between defining the column vectors of the matrix of transformation. The yellow box controls the column vectors defining the matrix of transformation. In particular, the green vector controls the first column vector and the blue vector controls the second column vector. By grabbing the ends of these two vectors, you can construct any 2x2 matrix.
Below the yellow box is a box that controls the vector x. As you move x (the red vector) about the domain of the transformation, you can watch both x and the image T(x) (the magenta vector) change in the large area to the right of the screen, depicting the codomain of the transformation. The movement of the vector T(x) depends on the nature of the matrix of transformation.
The large codomain region also displays information concerning the length of the vector x, the length of the vector T(x), the radian measure of the angle between these two vectors, and a lambda approximator. Two buttons at the bottom of this region control the display of the Eigen Equations in a red box above the codomain box.
Open Eigenizer in new window
Note: The "?" at the bottom right-hand corner of the workspace is a link to Key Curriculum Press and its About JavaSketchpad web page.
Sample Exploratory Activity:
This sample activity provides a guided exploration of eigenvalues and eigenvectors of a particular matrix and includes a set of questions that can be asked for any other matrix, as well as some general questions about the tool and observations made from interacting with the tool.
Given your exploration (and perhaps some additional ones), answer the following questions:
The tool allows students to explore specific matrices as well as hypothesize about possible matrices with particular properties. It is with the latter type of explorations that the worlds of geometry and computation can fuse. Students need to think beyond computations that MatLab might be able to perform and ponder the possibilities of "what if?".
Next page: 14. Transformer3D Tool and Sample Activity
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