### Review Sheet for Test 4 - Ch 1-4, 7, Computer Graphics
and Related LAMP Materials

**1 8.5 x 11 sheet with writing on both sides allowed.
You may put anything you want that fits on your sheet. **
Be sure to put the blue box on
p. 221, the 5 basic (but general) matrix transformation
froms from LAMP module 4 section 1
(projection, reflection, rotation, dilation and shears),
the forms at the bottom of page 370,
and vector space axioms 1 and 6 and their negations
(ie the subspace axioms),
the one proof (see below), and any
definitions from things we have done in the past that you don't know
by heart onto your sheet
(but,
you do NOT need the other vector space axioms or their negations).
Calculator allowed, but not necessary. You will sometimes
be asked to show by-hand
steps.

**Mainly study** Problem Set 7 Solutions on WebCT (they will go up
Saturday afternoon and your graded PS7 will hopefully be on my
door by Monday at 2),
LAMP Chapter 4 Module 1, and Test 3 Solutions on the handout I
gave you. Be sure to
also review
Test 1 and Test 2.
Many of the solutions to test
problems can be found in problem sets on WebCT.
**You need to also know big picture ideas**
- applications of matrices to real life, the purpose and usefulness of
various things that we have done in the class, and the major ideas
(not terminology or specific definitions though) in LAMP Ch 4 modules 2 and 3.

Two or three questions on the test will be on material from computer graphics,
and the other questions on the test will be on Ch 1-4, 7 and related material.

In addition to knowing how to set problems up and perform the relevant
by-hand calculations
(you need to be able to quickly multiply matrices by hand,
quickly take determinants by hand, quickly solve
systems of equations by hand and be able to find eigenvalues,
eigenvectors and the matrix P, if it exists, by
hand), quickly produce various transformation matrices and use them, and
you also need to know
examples and counterexamples.

Know the one proof:

6.1 p. 331 number 36 (we did this in class and gave more
explanation than the book) -
Prove that the general rotation matrix gives rise to a linear transformation
form R^2 to R^2 which has the property that it rotates every vector in
R^2 counterclockwise about the origin through the angle theta.

The test will be by hand.
Be sure that you know how to read and use the output given to you from Maple
on

with(linalg);

M:=matrix...

rref(M);

eigenvectors(M);

inverse(M);

evalm(A&*B);

evalm(inverse(P)&*A&*P);

and from items in Problem Set 7 Solutions and Chapter 4 Module 1.

Since there won't be time for revision, I will hand you solutions
to the test on your way out the door. An extra 20 points will be automatically
added to everyone's grade.