MATLAB Code:

Vectors:

First, choose 2 vectors (note that in the code above these two vectors are (0, 0) and (1, 2)) the terminal points of which are used to form a rectangle. Plot this rectangle using code similar to that provided above. Then choose TWO different matrices each of which performs a single geometric operation of your choice. In both cases, multiply your 2 vectors by these matrices and plot the resulting rectangles. Include one plot in your report which shows your original rectangle and your two transformed rectangles. Include the matrices you used to do the transformation.

Composition :

Verify the result of Problem A6 in Section 3.3 of the text; that the two compositions of a vertical shear and a stretch in the y direction, do not commute. Do this by plotting the image of the unit square with corners at (1, 1),(2, 1),(2, 2),(1, 2). Then plot the results of applying the COMPOSITION of the two operations (vertical shear and stretch) in both orders and showing that the resulting shape depends on the order in which the operations are applied. Corroborate your experimental proof of the non-commutability of these transformations by referring to Theorem 3.2.5 of the text (i.e., by considering the associated matrices)