A linear transformation of the form
maps each vector x = (x1, x2) into a vector y = (y1, y2).
In the Java applet below the vector x is marked by a red line and dot and the vector y is marked by a blue line and dot. You can see how y depends on x by clicking or dragging on the graph to change the value of x. The vector y will be changed based on the new value of x.
You can change the entries in the matrix A by clicking on each of their values at the right and typing the new value in the popup dialog box.
Investigate each of the following linear transformations visually using the applet above. Describe what the transformation does and note any noteworthy features.