MA 305 Bonus Homework

Due 12:00 pm on Tuesday May 13,  2003


The bonus homework is worth up to 75 pts added to your overall homework total. There will be no late submissions.

Calculations necessary for these problems may be done either by hand or with Maple. Solutions are to be submitted as a ASCII text (.txt) or Maple Worksheet (.mws) ,  file via WolfWare.

If you use Microsoft word, please save your file as ascii text with a .txt extension before submitting the file.

Submitted files should have either .txt or .mws extensions. This makes the grader's life much easier.

Incorrectly submitted files will result in NO CREDIT, so be sure the file you submit is readable in a text editor or Maple. If you are using Windows, check text files using notepad to make sure it looks readable.

Show no work and you will receive no credit. This means show all of your maple commands or if done by hand show most of the intermediate steps so we know how you arrived at your answer.

You must write up your own homework.  You may work together in the formulation of your answers, but you must type your  own file(i.e. no copying and pasting either).

Put your name and the names of all the people you worked with at the beginning of your submission file.

Questions about the assignment may be sent to the TA, Lauren D'Elia at  rldelia@unity.ncsu.edu


1.  Determine if the given functions are linear transformations. If it is a linear transformation, find the matrix A such that L(x)=A*x. If it is not a linear transformation, show why not.
    1. L([x,y,z]T)=[3x+2y-6z, -x+5z, 2y]T
    2. L([x,y,z]T)=[4x-7y+2z, 3x-z+1]T
    3. L([x,y,z]T)=[-3x+z, z - y, y, -x+2y]T


2. Let
[  1   2  -1  -2 ]
[  0   2   3  -2 ]
A = [  0   0   2   4 ]
[  0   0   1  -1 ]

  1. Without using the charpoly or the CharacteristicPolynominal command in Maple, compute the characteristic polynominal of A in factored form. (Note you can use the factor command in Maple).
  2. Find the eigenvalues of A without using the eigenvalue commands of Maple.
  3. For each eigenvalue of A find a corresponding eigenvector of A without using the eigenvector commands of Maple.
3. For the system of differential equations
du/dt = u+2w
dv/dt = -u +2v-3w
dw/dt = -w
do the following.
  1. Find the general solution to the system of differential equations.
  2. Find the particular solution that satisfies the initial conditions u=-2, v=2, w=3 when t=0.