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neila/matrixencryption.nb

Created November 21, 2020 14:11
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text encryption using simple matrix calculations
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matrixencryption.nb
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Removing the same column from a pair equivalent matrices will affect row \
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"\n\nSubtract 2\[Cross]row 1 from row 3:\nA = ",
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Row equivalent augmented matrices have the same solution set.\
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Since they are row equivalent, the RREF form will be the same and thus can be \
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Augmented matrices with the same solution set are row equivalent.\
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First, I assumed that what goes in the roundabout comes out of the \
roundabout. This applies to both roundabouts as well as the one-way roads. \
There should be no cars parked at any point within our system. I also assumed \
that cars would actually follow the one-way rule on the road, unlike India."
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"As computed above, the number of vehicles that will use each road segment \
in the proposed system every hour is:\n",
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"\n\n(NOTE: I tried very hard and spent a very large amount of time trying \
to solve this augmented matrix in matrix form, but could not find a way for \
Mathematica to compute a combination of variables without using negative \
values. As the number of cars cannot be negative, I had to find a different \
way to solve. With 7 variables and 6 equations, the system is underdetermined \
and here, it has infinitely many answers.)"
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The roads in total will need to accommodate about 1000 cars in total, per \
hour. However, as the solution shows, there is a polarization of the roads \
which cars travel in. Cars travel by far the most in the vertical roads \
(c,d,e) while only some in (f,g) and none in (a,b). For example, if we look \
at the upper-rightmost roundabout, all cars that go out are exclusively from \
road e. The traffic might congest, but if some of those people who wanted to \
get out from the roundabout came from b, there would be less cars needed to \
use road e. Cars should be encouraged to follow routes a and b especially, \
and avoid d and e.\
\>", "Text",
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Looking at the list above, Segments a and b can be totally closed and still \
maintain traffic flow predicted by the electronic sensors.\
\>", "Text",
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Cell[TextData[{
"The system of linear equations that describe the traffic after large events \
(with the same assumptions as part a) are:\n\n",
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We see that due to the event, we observe an increase in traffic particularly \
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It is interesting that we want to minimize the use of segment a in order to \
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\[CloseCurlyDoubleQuote] But this type of analysis helped me understand that \
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