Activity 4: Matrices as linear transformations


Use the applet below to explore the geometric effect of the matrix T on the unit cube shown on the 3D view. 1. Click the button Apply T. 2. Then slowly drag the slider that will appear. As you do, pay attention to the transformed cube, the values of the matrix and its determinant. Note: After applying T, you can change the position of the cube. Just drag the point that will appear on its corner. Click on it to toggle moving up-down & left-right.

What do you notice? What do you wonder? List any observations you see below.

Describe a relationship between the volume of the transformed cube, the determinant of T, and the unit cube.