Assignment For Section 2.4

You should read the section before attempting any reading questions or problems. Remember that you are responsible for all definitions and examples. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)   Define the following in your own words.
a)    span            b)    parallelepiped            c)    rotation matrix            d)    dilation

2)   Explain the difference between a dilation and a coordinate rescaling.  What shape will you get if you perform a dilation on a sphere?  What shape will you get if you perform a coordinate rescaling on a sphere?

3)   The text shows that invertible linear transformations preserve parallelograms and discusses how these transformations alter the area of the parallelogram.  Since a triangle is half of a parallelogram similar results should apply to a triangle.  Show this by answering problem #6 and #7 from page 141.

Problems:

page 141     2, 3, 8, 10, 11a, 12a,b, 13, 15, 20