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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: Yendall on October 20, 2012, 06:05:53 pm

Title: Matrices Interpretation
Post by: Yendall on October 20, 2012, 06:05:53 pm: Hey, sorry another question:
(http://i292.photobucket.com/albums/mm37/yendall_2008/awd_zps316b7976.jpg)
How I interpret this question is that he can guess 1 of 4 answers initially.
So I used test data to find out what each answer will give on the next question:
Guessing for the first question:
Guessing A:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}*\begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix}$
Guessing B:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}*\begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix}$
Guessing C:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}*\begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix}$
Guessing D:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}*\begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix}$

If you guess A, the answer will be A.
If you guess B, the answer will be D.
If you guess C, the answer will be B.
If you guess D, the answer will be D.
Guessing for the second question:
Guessing A:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^2*\begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix}$
Guessing B:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^2*\begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix}$
Guessing C:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^2*\begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix}$
Guessing D:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^2*\begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix} = \begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix}$
If you guess A, the answer will be A.
If you guess B, the answer will be C.
If you guess C, the answer will be D.
If you guess D, the answer will be B.
Guessing for the third question:
Guessing A:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^3*\begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix}$
Guessing B:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^3*\begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix}$
Guessing C:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^3*\begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix}$
Guessing D:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^3*\begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix}$
If you guess A, the answer will be A.
If you guess B, the answer will be B.
If you guess C, the answer will be C.
If you guess D, the answer will be D.
Guessing for the fourth question:
Guessing A:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^4*\begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}1\\ 0\\ 0\\0\\ \end{bmatrix}$
Guessing B:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^4*\begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix}$
Guessing C:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^4*\begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix} = \begin{bmatrix}0\\ 1\\ 0\\0\\ \end{bmatrix}$
Guessing D:
$\begin{vmatrix}1&0&0&0 \\ 0&0&1&0\\ 0&0&0&1 \\ 0&1&0&0\end{vmatrix}^4*\begin{bmatrix}0\\ 0\\ 0\\1\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 1\\0\\ \end{bmatrix}$
If you guess A, the answer will be A.
If you guess B, the answer will be D.
If you guess C, the answer will be B.
If you guess D, the answer will be C.

The only trend i've picked up on is that the first question will always be A. This doesn't fit any of the answers, what am I missing?
Title: Re: Matrices Interpretation
Post by: lukaal340 on October 20, 2012, 06:24:48 pm: I think the answer is B. if he guesses -
A first A-A-A-A
B First B-D-C-B
C First C-B-D-C
D First D-C-B-D
the first and fourth are always the same.
Title: Re: Matrices Interpretation
Post by: Yendall on October 20, 2012, 06:42:22 pm: How did you determine that?
Title: Re: Matrices Interpretation
Post by: lukaal340 on October 20, 2012, 06:54:20 pm: He can guess either A,B,C or D to start off. If he guesses C for example, by looking at the transition matrix we can see his next guess will be B. Then we look in the B column and can see the third guess will be D. In the D column it tells us his fouth guess will be C, hence C-B-D-C. I hope that makes sense. Dont worry about using matrices to work it out, just do it by eye and with a pen and paper.
Title: Re: Matrices Interpretation
Post by: Yendall on October 20, 2012, 06:55:39 pm: Oh my god that does make sense. Thanks heaps dude.