MI4
Project
Due: Nov. 24, 2015
At beginning of class
Matrices and Transformations.
Writing Assignment Guidelines:
For this assignment, you are to work with one other student (from the same class) to
collaborate and develop your solutions. You will submit one paper per pair; electronically
to turnitin.com.
You are to write your solutions carefully and completely. The primary purpose for this
assignment is to emphasize your ability to explain your mathematical work clearly, as if
you were writing this problem to a fellow MI-4 student who knows as much mathematics
as you; but has not done this project. When writing about mathematics, it is most often
very illustrative to include examples and figures.
Your paper should include the following:
 Good drawing(s) with labels. Can be done by hand, or on the computer with your
choice of software. If done by hand, drawings must be neat and accurate.
 An explanation of your set-up and the work done.
 Correct and precise mathematics, paying particular attention to the clarity of your
work.
 Generalizations supported by your work, with sound justifications written in
complete sentences.
Writing style and clarity will be a factor in your evaluation.
IMSA
F15
MI4
Project
Due: Nov. 24, 2015
At beginning of class
Transformations and Matrices
Do one of I or II below.
I. Discussion of matrices that reflect vectors over lines.
A. Find a matrix that will reflect vectors over the line y  2 x .
B. Generalize your solution for any line that passes through the origin, y  mx .
C. Find a matrix for reflecting vectors over the line y  mx  b .
D. Prove that reflection over a line (through the origin) preserves distances. That
is, if you reflect a vector v over the line y  mx , then the image of v has the
same length as v .
II. Discussion of matrices that rotate vectors through an angle  .
A. Use matrix and vector techniques to find a transformation that will rotate by
angle  counter-clockwise around an arbitrary point (a, b) in the plane.
B. Prove that rotation through an angle  preserves angles. That is, if the angle
between u and v is  , then the angle between their images is also  .
8
6
A
4
B
A'
2
C
-10
-5
5
C'
10
B'
-2
-4
-6
-8
IMSA
F15