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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: Studyinghard on November 02, 2010, 10:42:46 am

Title: Matrices Mass. Confusion
Post by: Studyinghard on November 02, 2010, 10:42:46 am: Insight 2006 Question 3c

The fishing village has two newspapers, The Globe and The Bugle. The newsagent records the
numbers of each paper that are sold.
On the first day the newsagent notes that 26% of the newspapers sold are copies of The Bugle.
On the second day, the newsagent notes that 60% of the people who bought The Globe on the
first day buy it again on the second day and the rest buy The Bugle. By contrast, only 5% of
customers who bought The Bugle on the first day change to The Globe on the second day. The
newsagent finds that the trend continues in this fashion.

a. Write the initial state matrix as a column matrix, putting The Globe in the first row.

Answer [0.76]
[0.24]

b. Write the transition matrix that represents this situation.

0.6 0.05
0.4 0.95

c. On the fifth day of this study the newsagent sells 599 newspapers. Calculate the number of copies of The Globe sold on this day.

So it says do T^4 times initial as the initial counts as first day.

Now Insight 2008 Matrices q4
Similar question

During the first week of monitoring Frank’s Fruit Mart there were 875 packs purchased in
total. In the same week, 215 standard fruit packs and 512 family fruit packs were purchased.
b. Write this information in the form of an initial state column matrix, I0.

215
512
148

Determine the expected number of Standard, Family and Bulk fruit packs purchased in
the third week. Give your answers to the nearest whole number.

So following logic from the 2006 you would do T^2 times initial right. Apparentally not :s

Can anyone explain?
Title: Re: Matrices Mass. Confusion
Post by: LFTM on November 02, 2010, 10:47:39 am: I get confused with this as well, even in methods.
Title: Re: Matrices Mass. Confusion
Post by: Studyinghard on November 02, 2010, 03:12:03 pm: bump
Title: Re: Matrices Mass. Confusion
Post by: ghadz7 on November 02, 2010, 03:23:21 pm: Is it 26% or 24% ?
Title: Re: Matrices Mass. Confusion
Post by: Studyinghard on November 02, 2010, 03:27:17 pm: 26 actually, either way whats the method the answer doesnt really matter .
Title: Re: Matrices Mass. Confusion
Post by: ghadz7 on November 02, 2010, 03:32:04 pm: The 2008 question was pharsed incorrectly. They should have clarified whether it is towards the start of the week or end of the week. I think VCAA should be more precise.
Title: Re: Matrices Mass. Confusion
Post by: plato on November 02, 2010, 06:07:34 pm: In your first example, you may want to adjust the typo between 26% and 0.24 in the matrix.
You may see that the power for the transition matrix is 4 and not 5 by considering the following:
In week one, the state matrix is $\left[\begin{array}{c}0.76\\ 0.24\\ \end{array} \right]$
This is then $S_1$ and not $S_0$

Then, $S_2=T\times S_1$ to give the state matrix for the SECOND week
and $S_3=T\times S_2 = T^2\times S_1$ for the third week and ultimately:
$S_5=T\times S_4 = T^2\times S_3 = T^3\times S_2 = T^4\times S_1$
Title: Re: Matrices Mass. Confusion
Post by: Studyinghard on November 02, 2010, 08:44:01 pm: Okay so what about the insight 2008 question. It follows the same logic but is a different answer
Title: Re: Matrices Mass. Confusion
Post by: onerealsmartass on November 02, 2010, 08:45:26 pm: they probably did something wrong.
vcaa wont be that ambiguous...