a.)
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where and => observation 1
*Note: that they (a and b)are multiplied by the matrix ( 3 and 1 )of P1 *
Example:
b.)
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Where and => observation 2
*Note: They too are multiplied by 4 and 2 the matrix of S1 *
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For Pn I have observed the pattern “observation 1” and in where x is doubled the previous value the pattern of x= 2, 4, 8, 16, 32… and “a” would always be twice bigger/higher and “b”. where b=a-2.
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For S1 I have also observed a pattern “observation 2” and in where x is again doubled the previous value except for the fact that it skips x=4 but then it does continue on as normal having the pattern of x= 2, 8, 16, 32…
Also “c” would always be 1 number higher than “d”. where d= c-1.
3.) Now consider the matrices of the form:
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I have observed a pattern that as k increases “a” always remain twice higher than “b” where b=a-2;. “a” and “b” increases as in a sequence, the previous “a” matrix is 1 number less than the next “a” in the next matrix; same goes for “b” and so the pattern goes:
a = 2, 3, 4, 5, 6, 7, 8, 9…
b = 0, 1, 2, 3, 4, 5, 6, 7…
4.) Use Technology to investigate what happens with the further values of k and n.
in where and .
There is no limit to k and n.
5.) Explain why your results hold true in general:
Well I believe that my results hold true in general because the pattern I have been studying works will all the matrices I have tried it with. I have also used technology to see if my answers and observations were correct, in fact I was not mistaken.
