Concepts like the determinant, eigenvectors, and eigenvalues can be difficult for students in a beginning linear algebra course to understand and visualize. This talk will present a series of labs that allow students to generate and work with  visual representations of linear transformations, determinants, eigenvectors and eigenvalues.



Summary:

I will present the following Geometer’s Sketchpad labs:

Visualizing Linear Transformations Understanding image, range, kernel, and projection.

Determinants and Orientation Relating the determinant of a matrix to the orientation-preserving or -reversing property of the corresponding linear transformation.

Determinants and Areas Relating the determinant of a matrix to the area of the image of a unit area under the corresponding linear transformation.

Eigenvectors and Eigenvalues Understanding that for some linear transformations, certain vectors are mapped to multiples of themselves.