Effect of a 3x3 Singular Transformation Matrix on 3D Space
This Demonstration shows the effect of two 3×3 nonzero singular transformation matrices on 3D space: all points in 3D space are either mapped to a line or plane passing through the origin. Use the sliders to vary the coordinates of the point in the plot on the left and observe its corresponding image point in the plot on the right.[more]
When the three columns of the singular matrix are all scalar multiples of one another, the image of is a line; otherwise it is a plane.[less]
Transformation matrices are usually studied by pure math students in high school in certain countries.
 L. Bostock, S. Chandler, and C. Rourke, Further Pure Mathematics, Cheltenham, UK: Stanley Thornes, 1990.