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Matrix Binomials t2

Extracts from this document...

Introduction

IBO Internal Assessment

Mathematics SL Type 1

Matrix Binomials

image01.pngimage02.png

Pilar Dell’Oro -003

February 2008

        This assignment of my portfolio is to allow me to deal with matrix binomials and to investigate them through finding a series of statements.

        Through my knowledge of algebra, matrices and sequences I will try to investigate these affirmations to find any relationships or patterns.

        Through the use of both my TI 83 scientific calculator and the math type program.

Introduction

        Matrix comes from a Latin word that means womb; and so where something is formed and produced. A matrix is a rectangular arrangement of numbers.[1]

        The term "matrix" was thought up by some very famous mathematicians such as J. J. Sylvester. Cayley, Hamilton, Grassmann, Frobenius and von Neumann who helped with the development of matrices in 1848.

        Since their first appearances long ago in ancient China (650 BC), they have remained very important mathematical tools. They are used for general arithmetic, in quantum mechanics, engineering, dance routines and many other areas which are surely unexpected.

image77.jpg

image83.pngimage92.pngimage17.pngimage02.png

Knowing the values of image80.png andimage81.png, I can then go on to calculate image107.png andimage03.png.

In order to facilitate all my workings out, I will do this on my graphical display calculator.

image10.png

image18.png

image25.pngimage32.png

image40.pngimage49.png

image60.png

image71.png

image78.pngimage76.png

image79.png

...read more.

Middle

image97.png

Gdc

image98.pngimage05.pngimage05.pngimage98.png

Therefore, knowing and, we can now find.

Assuming image99.png

We can take as an example:

image100.png

Let’s check our general statement for with the following example.

image101.png

Letting and image102.pngwhen image103.pngare constants: By different values of these constants we can find the following:image104.png.

With this I am going to change the constants of image14.pngcouple times to calculate the other components necessary. With the use of my gdc.

image105.png

image02.png

Constant -10


image06.pngimage106.pngimage05.pngimage110.pngimage108.pngimage05.pngimage109.pngimage05.png

Constant 5

image06.png

image111.pngimage112.png

image04.png

image05.pngimage05.pngimage05.png

Constant 18

image06.png

image07.pngimage08.pngimage09.png

image05.pngimage11.png

image05.pngimage05.png

image12.png

We substitute powers instead of numbers.

image13.png

...read more.

Conclusion

  • Matrices can be used to encrypt and decrypt codes; that believe it or not are still in use. Have you ever noticed in hotels when they give you a safe in your closet? Well, if you ever happen to forget the code you put into it, they bring a machine up to your room that functions upon matrices and they decrypt your code.
  • They are used in fields such as plumbing, engineering and traffic issues because they can be used to display networks allowing calculations to be worked out easily.
  • When realizing you can solve simultaneous equations by matrices, didn’t you feel a sudden relief?
  • They are used in graphics, and in areas such as cartoon animation and computer/video games such as Nintendo and Wii.  

Matrices are used overall in math and science but they surely do find a way to save people from a lot of calculations and saves them time.


[1] Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, chapter  1.1

...read more.

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