### Select Hints and Commands on PS 3

Using with(LinearAlgebra):

** >M:=Matrix([[... **

** >Determinant(M);**

From the main web page,
see the hints for Problems Sets 1 and 2 for a review of the other
Maple commands...
Also see Practice Problem Solutions for 2.5 and Chapter 3,
which are on ASULearn.

**Problem 1:** **2.5 number
24**
Use the fact that you know the code -19, -19, 37, 16 decodes to _SUE.
ie

[-19,-19] Matrix([[a, b], [c,d]]) = [_ S converted to numbers] = [0 19]

You will have a corresponding equation for 37, 16 -> UE.
Obtain a system with 4 equations and 4 unknowns, the entries of the
decoding matrix.
Then solve for the decoding matrix and you can apply it to the rest
of the message to decode it. You will know if you did this correctly
if your decoded messages converts to an alphabet string that makes sense.

**Problem 2:** **Healthy/Sick
Workers (In Maple)**
See the Practice Problems in 2.5 and 3.1-3.3
Solutions on ASULearn to review 2.5 number 10 as well as the
Your text comments and commands need to all be in Maple for this problem.

In **part a**, be sure that you have the correct matrix N:
the matrix is one that has the columns adding to
1, matrix multiplication units matching.
The fact that the percentage of healthy workers are the
first component of the state vector uniquely defines the matrix where the
first column is

Healthy->Healthy

Healthy->Sick.

Be sure to use **fractions**
since Maple can have problems with decimals.

In **part c**, form the augmented matrix for
the homogeneous system

(I-N)x=**0**

Our shortcut is to add a row of 1s to the augmented matrix as
we did for 2.5 #10 to represent the fact that the healthy and sick
workers add to 100%. Be sure to add the row of
1s **after** you first subtract N from
the identity from N and augment that with 0s - namely the 33 bottom right
entry is a 1.
Then use the ReducedRowEchelonForm command.

In **part d**, first define the a column vector U
using that 15 are sick
(the second component). Now apply N the correct number of times
to it to obtain Tuesday, etc... You can use commands like

**evalf((N^50).U);**

by changing 50 to the number to the number of days you want.

**Problem 3:**
**3.1 number 47a.** This statement is false. It is
not sufficient to just say that the book has a statement which differs a
bit - both statements are true for some [but not all] matrices.
Produce a counterexample to show that the statement is not true for every
matrix. Pick a 2x2 matrix with some specific numerical entries whose
determinant is different from what is listed in the false statement
and show work.

**Other true/false statements** are similar - if it is false, then
produce specific examples
where the statement does not hold. Try to choose easy examples -
for example with lots of 0s and 1s. For true statements, find a general
reason it always holds from the book and quote the book statement.