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Exercise 1:
In Chapter 7, you briefly learned about how
matrices can be used for creating secret codes. Go to the Cryptography Internet Project to
learn more about coding. Read the first page and, then, follow the basics and Enigma machine links.
For the "basics" link, read the first section and "Substitution ciphers and
decoder rings." For the "Enigma machine" link (this may take a little while
to load), create a secret message to turn in to your instructor. If you change the
machine's settings, be sure to turn in the new settings too. |
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Exercise 2:
Go to the Linear Equations
Solver and enter in the following system:
52x + 17y - 93z =
-332
-74y + 36z = 834
45x + 25y + 12z = 1254 |
(Once
again, each equation is to be entered in the form:
ax + by + cz = d
The blanks are set up so that you enter the
values for a, b, c and d.)
Note that the determinant of the
coefficient matrix is provided along with the values of x, y and z. If you had been using
Cramer's Rule to solve this system, what would the values of the other three determinants
have been? |
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Exercise 3:
As we've mentioned previously, matrices aren't
really meant to be done by hand. They are made for solving enormous systems of equations
with huge numbers of unknowns. To see a set of real-world matrices and their uses, go to The Matrix Market and follow
the applications link.
| 1) |
Select "Air Traffic
Control" and submit your query. Follow the ZENIOS link. What is the size of this
matrix? |
| 2) |
Select "Nuclear Reactor
Design" and submit your query. Follow the NNC1374 link. What is the size of this
matrix? |
| 3) |
Select "Oceanography"
and submit your query. Follow the PLAT1919 link. What is the size of this matrix? |
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