Action of a 2x2 Singular Transformation Matrix in 2D

transformation:

2D space mapped to a line by

a	b
c	d

=

1.	2.
3.	6.

a

1

b

2

c

3

This Demonstration shows the action of

22

singular transformation matrices in 2D: all points are either mapped to a line passing through the origin or, if the matrix is null, to the origin itself. Use the sliders to vary three of the elements of the singular matrix.

When the 2D space is mapped to a line, drag the locator to move the point on the left and observe its corresponding image point in the plot on the right.