Assignment for Week 11/20-11/22

Reading: Read Section 4.1 for 11/22

Written Assignment 7 (Due Wed 11/22) is in TWO PARTS
Turn it in as two assignments stapled separately

Assignment 7A (note this was modified on 11/21)

Do any 5 problems from this set of 10 problems:

• Section 3.8: Problems # 2, 6, 10, 16, 18
• Section 4.1: Problems # 2, 6, 10, 16, 18

Assignment 7B Experiments

In 7.1 and 7.2 you will be given or will choose a matrix denoted A or B etc. Also, you will be given a
vector X. The numerical experiment is to compute a sequence of ten vectors (with a calculator or software, not
by hand!). Suppose your matrix is denoted by A and your vector by X:

• Start with setting X_0 = X.
• Then compute X_1 = AX_0
• Then compute X_2 = AX_1
• Then compute X_3 = AX_2
• Continue computing until you reach X_10 = AX_9

As results to report, write down your A and a table of the vectors you computed.
Study the vectors and see whether you can guess what A_100 might be.

• Do the experiment again with the same A and a different vector Y OF YOUR CHOICE to get a sequence of
  vectors Y_0, ... Y_10 as before.

Now look for patterns. Can you see a relationship between X_10 and Y_10 that might become more
pronounced if you computed a longer sequence?

Write a few sentences reporting what you observe and any conjectures you may wish to make.

Problem 7.1

Do the experiment with matrix A, where A is the matrix with first column [.8 .2]^T and second
column [.2 .8]^T.

• Set X = [1 2]^T for the first run of the experiment.
• Pick a Y of your own choosing and run the experiment again.

Problem 7.2

Do it again with matrix B with columns [.9 .1]^T and [.8 .2]^T and X = [4 5]^T.

• Then again pick a Y of your own choosing and run the experiment again.
  Again write observations.

So after both 7.1 and 7.2 you will have 4 tables of data.