Date 
WORK DUE at the beginning of class or lab
unless otherwise noted!
For practice problems, make sure that you can present and/or
turn in your work  write out the
problem and the complete solution  show work too!

July 1  Fri 

__________ 
________________________________________________________________________

__________

________________________________________________________________________

June 30  Thur 
 Final project abstract due by 12 noon
as an attachment onto WebCT that I can read (text, Word, rtf, or Maple)

June 29  Wed 

June 28  Tues 
 Final project proposal (a short description of what you plan to do)
and preliminary list of references due. Your topic needs to be preapproved
as there is a limit to the number of people per topic.
 Study for test 3 and write down any questions you have.

June 27  Mon 
 Problem Set 6 
See Problem Set Guidelines and
Sample Problem Set WriteUps
*7.1 #14 by hand and on Maple via the
Eigenvectors(A); command 
also compare your answers and resolve any apparent conflicts
or differences within Maple text comments.
*Rotation matrices in R^{2}
Recall that the general rotation matrix which rotates vectors in the
counterclockwise direction by angle theta is given by
M:=Matrix([[cos(theta),sin(theta)],[sin(theta),cos(theta)]]);
Part A:Use only a geometric explanation
to explain why most rotation matrices have no eigenvalues or eigenvectors.
Part B: Apply the Eigenvalues(M); command. Notice
that there are real eigenvalues for certain values of theta only.
What are these values of theta and what eigenvalues do they produce?
Find a basis for the corresponding eigenspaces.
(Recall that I = the square root of negative one
does not exist as a real number and that
cos(theta) is less than or equal to 1 always.)
*7.2 7, 18, and 24
*Foxes and Rabbits (Predatorprey model)
Suppose a system of foxes and rabbits is given as:
Write out the Eigenvector decomposition of the iterate x_k, where the
foxes F_k are the first component of this state vector, and the rabbits
R_k the second. Use the decomposition to explain what will happen to x_k in
the longterm.
Extra Credit: Determine a value of the [2, 2] entry that leads to constant levels of the fox and rabbit populations, so that eventually neither population is changing. What is the ratio of the sizes of the populations in this case?

June 24  Fri 
 Test 1 revisions due
 Test 2 on Chapters 13 and 4.
Study Guide

June 23  Thur 
 Review for test 2 and write down any questions you have.
 Read over the final project links under the July 1 due date.
 Begin working on Problem Set 6.

June 22  Wed 

Jun 21  Tues 
 Practice Problems (to turn in) 4.4 numbers 11, 53
4.5 number 22 4.6 numbers 22, 31
 Work on Problem Set 5

June 20  Mon 
 Problem Set 4
See Problem Set Guidelines and
Sample Problem Set WriteUps
4.1 36 and 44
Cement Mixing (*ALL IN MAPLE*)
Hints for this problem
This problem is worth more than the others.
4.2 (19 and 20
If it is a vector space then just state that it is because
it satisfies all of the vector space axioms , but if it is not, then write out
the complete proof that one axiom is violated as in class)
Natural Numbers Prove that the natural numbers is not a subspace
of R.
Solutions to 2x3y+4z=5
Prove that the subset of R^{3}
consisting of all solutions to the equation
2x3y+4z=5 is not a subspace of R^{3}
4.3 (14 parts D, E, and F
if it is a subspace then just state that it is because it is closed under
addition and scalar multiplication, but if it is not, explain in detail by
showing
that one of these is violated, as in class. Also, as I mentioned, be sure to
leave n as general  do not define it as 2)
Extra Credit
Prove that the subset of R^5 consisting of all the solutions of the
nonhomogenous equation Ax=b, where A is a given 4x5 matrix and b is a
given nonzero vector in R^4 is not a subspace

Jun 17  Fri 

Jun 16  Thur 
 Practice Problems (to turn in) 4.1 numbers 7, 35, 43, 49, 52,
4.2 numbers 21 and 22
 Study for test 1 and write down any questions you have.

June 15  Wed 

Jun 14  Tues 
 Practice Problems (to turn in)
2.5
number 10 and 16, 3.1 number 33 (byhand), 3.2 number 25
(byhand), and
3.3 number 31.
 Work on PS 3

Jun 13  Mon 
 Problem Set 2  See
Problem Set Guidelines,
Sample Problem Set WriteUps,
and
Maple Commands and Hints for PS 2.
I also encourage you to ask me questions about anything
you don't understand in office hours or on the WebCT bulletin board.
2.1 (26 byhand and on Maple), 30
2.2 (34 parts a, b and c)
To show that the following statements about matrices are false,
produce counterexamples and show work:
Statement a) A^2=0 implies that A = 0
Statement b) A^2=I implies that A=I or A=I
Statement c) A^2 has entries that are all greater than or equal to 0.
2.3 12, (14 by hand and on Maple), 28a, (40 parts c and d)

Jun 10  Fri 
 Practice Problems (to turn in) 2.1 numbers 7, (9, 11, 15, 32 byhand),
2.2 numbers 17, 18, 35.

Jun 9  Thur 

June 8  Wed 
 Read section 1.2
 Practice Problems (to turn in) LarsenEdwards
1.2 numbers 13, 15, 17, 19, 21, 25, 27, 43, 49
(do these byhand since you need to get efficient at the byhand method

answers to odd problems are in the back of the book  it is your job
to show work).
 Continue working on problem set 1.

June 7  Tues 
 Read p. xv and section 1.1
 Practice Problems (to turn in at the start of class) LarsenEdwards
1.1 Do the following byhand since you need
practice on this (but you may use a calculator or Maple on 19 and 53)
numbers 7, 15, *19, 53*, 57, 59, 61, 73
(answers to odd problems are in the back of the book  it is your job
to show work).
 Begin working on problem set 1.
