Transformations l1–l8 refer to the linear transformations from the opening exercise. for each pair:
i. make a conjecture to predict the geometric effect of performing the two transformations in the order
specified.
ii. find the product of the corresponding matrices in the order that corresponds to the indicated order of
composition. remember that if we perform a transformation lb with matrix b and then la with matrix
a, the matrix that corresponds to the composition la ∘ lb is a. that is, lb is applied first, but matrix b
is written second.
iii. use the geogebra applet transformcubes. ggb to draw the image of the unit cube under the
transformation induced by the matrix product in part (ii). was your conjecture in part (i) correct?
a. perform l6 and then l6.
b. perform l1 and then l2.
c. perform l4 and then l5.
d. perform l4 and then l3.
e. perform l3 and then l7.
f. perform l8 and then l4.
g. perform l4 and then l6.
h. perform l2 and then l7.
i. perform l8 and then l8.