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Investigating Matrices

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Introduction

April 13, 2008

Investigating Matrices

 1.) Calculate Mn : n = 2, 3, 4, 5, 10, 20, 50

  • Pattern I found was that  as n increases x is doubled the previous value while the matrix remains as .
  • Example:
  • Another pattern with the matrices was that  and as n increases a is doubled  as zero “0” remains unchanged.

Example:

2.) Consider the matrices :

a.)

  • where and => observation 1

*Note:

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Middle

image00.pngWhere  and => observation 2

*Note: They too are multiplied by 4 and 2 the matrix of S1 *

  • 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.
  • For S1  I have also observed a pattern “observation 2” and  in where x is again
...read more.

Conclusion

k and n.
  • For k=10:

 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.

...read more.

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