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Monday, February 20, 2006 


So far, I've got a pretty good understanding of everything we've done on matrices.
Something that I found hard but now understand, was the question about 'stopovers' on the pre-test that we had on friday. I was very relieved when Cait said that she didn't know what the explanation was because in class today Mr. K went over it * THANKS Cait =) * .

The question asked: A network matrix, N, shows direct routes between cities. Which matrix calculation determines the number of routes with exactly k stopovers between two cities in the network? The answer was c) Nk + 1. See the thing is, N represents the direct routes. but we want to know what matrix is correct when using 'k' stopovers. Basically, the number of routes there are, is one less than the number of cities.

For example;
If you were trying to get from city A to city D, but there were no direct flights from A to D and you had to go through city B and city C...then that would mean that city B and city C are the two stopovers and city D is the destination which is the plus one.

[city b and city c] = 2 stopovers = k    
and [city d] = destination = +1

So..if I understood right, from the 4 cities (A, B, C, and D), there would technically be 3 'stopovers'...?

So if there were 5 cities, there would be 4 stopovers.
If there were 20 cities, there would be 19 stopovers.
And vice versa, if there were 15 stopovers, there were 16 cities.

When Mr. K explained the whole thing, then kept giving examples like those, it suddenly clicked! Well, I'm not entirely sure if I actually explained it correctly, but I think I get it now.

Oh, there was also one more thing that i'm not very clear on..there was this one problem on the board, that was done last week. It had to do about the population in 'mathland'. Here's the gist of it. There are 25 million people in total; currently, 10 million of them live in the city, 8 million live in the suburbs, and 7 million live in the rural area.
This was also given:
    C           S          R
C [ 65% 31% 4% ]
S [ 18% 70% 12% ]
R [ 7% 8% 75% ]

I know how to do the transition matrix, but for some reason, I still don't know how to formulate the state matrix for these kinds of problems..BUT other than that, everything else is going okay. Well, that's my blog for this unit =)

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