2x2 Linear Transformations
All of these files are intended to illustrate visually some basic concepts covered in a Linear Algebra Course. These files were used in the 2008 University of Cincinnati MAT Technology Summer Course.
Contents |
Image of a Point
This file, 
The Image of a Point, illustrates how the coordinates of the preimage (with respect to the original axis) are the same as the coordinates of the image (with respect to the transformed axis). This sketch also illustrates how the the rectangle formed by the preimage is transformed into a parallelogram whose sides lie on the column vectors. The area of this parallelogram is equal to the product of the area of the rectangle and the determinant of the matrix formed by the column vectors. This file also shows the image of the lattice points for reference.
Images of F
This file shows 
The Image of F under different linear transformation. There is a paper worksheet that accompanies this dynamic worksheet 
HERE.
Eigenvalues and Eigenspaces
An example of the Eigenspaces of 2x2 Matrix transformation.
Determinants
This dynamic worksheet illustrates the relationship between the DETERMINANT, the area of the pre-image, and the area of the image.
