Problem 11E

A rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations, which can speed up calculations that determine how a graphic image actually appears in terms of screen pixels. (The screen consists of rows and columns of small dots, called pixels.) The first transformation A1 shears vertically and then compresses each column of pixels; the second transformation A2 shears horizontally and then stretches each row of pixels. Let

and show that the composition of the two transformations is

a rotation in

Solution

Step 1

In the Question it is given that A rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations, which can speed up calculations that determine how a graphic image actually appears in terms of screen pixels. (The screen consists of rows and columns of small dots, called pixels.) The first transformation A1 shears vertically and then compresses each column of pixels; the second transformation A2 shears horizontally and then stretches each row of pixels. Let

and show that the composition of the two transformations is

a rotation in