• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16

# Matrix Binomials t2

Extracts from this document...

Introduction

IBO Internal Assessment

Mathematics SL Type 1

Matrix Binomials

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.

Knowing the values of  and, I can then go on to calculate  and.

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

Middle

Gdc

Therefore, knowing and, we can now find.

Assuming

We can take as an example:

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

Letting and when are constants: By different values of these constants we can find the following:.

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

Constant -10

Constant 5

Constant 18

We substitute powers instead of numbers.

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

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Extended Essay- Math

L& }ï¿½sï¿½ï¿½ï¿½ï¿½7K6Èï¿½;ï¿½ï¿½ï¿½-ï¿½ï¿½,ï¿½ \'ï¿½ï¿½[email protected]^ï¿½'ï¿½ï¿½-wRï¿½(c)ï¿½GWn1/4\$^@[email protected]'ï¿½>Òï¿½0"ï¿½ï¿½U`ï¿½ï¿½ï¿½...X&ï¿½\$]H K4ï¿½ï¿½"ï¿½BHï¿½aï¿½...ï¿½'hx ï¿½ï¿½[email protected]'ï¿½3ï¿½b~bï¿½z "Xdï¿½2yï¿½,ï¿½ [email protected]/43Gï¿½ï¿½1/4>ï¿½KDï¿½ï¿½?ï¿½ï¿½ï¿½ï¿½ï¿½[email protected]]ï¿½)Rï¿½Zï¿½&ï¿½ ï¿½ï¿½ï¿½8bUï¿½ï¿½ï¿½ [email protected]'1ï¿½ ï¿½":\ï¿½m"&ï¿½ ψW' ï¿½BRï¿½V8ï¿½ï¿½" ...E ï¿½]~ï¿½ ï¿½ï¿½% ï¿½BOa0ï¿½ï¿½L*ï¿½xï¿½ï¿½6ï¿½tï¿½ï¿½ï¿½ H ï¿½ï¿½.\$Ekï¿½ï¿½ï¿½Õ`R! ï¿½ï¿½Xï¿½ï¿½[email protected] ICï¿½ ï¿½ï¿½ï¿½<Vï¿½| 0ï¿½ï¿½H ï¿½ï¿½.\$Es`ï¿½ï¿½;ï¿½ï¿½'ï¿½"ï¿½"ï¿½[email protected] ï¿½ï¿½ï¿½fï¿½ï¿½ï¿½Hï¿½'Kï¿½ï¿½ï¿½[email protected]ï¿½ï¿½ï¿½x'8ï¿½["ï¿½,' \ï¿½ï¿½.1/4ï¿½ï¿½ï¿½Ä±Pï¿½jFï¿½ßï¿½rï¿½ï¿½- ï¿½(tm) ï¿½bï¿½ï¿½ï¿½Eï¿½3Gdï¿½ï¿½Wï¿½ï¿½...ï¿½' Ðï¿½ï¿½Dï¿½ï¿½5ï¿½ï¿½9r R`(tm)H`fz'QQï¿½xnï¿½ï¿½ï¿½ï¿½ï¿½gFï¿½OIï¿½dz'ï¿½......ï¿½ï¿½ï¿½...+#ï¿½Lï¿½ ï¿½(tm) "ï¿½ï¿½#ï¿½NGï¿½Qï¿½ï¿½1/4ï¿½ï¿½ï¿½ï¿½Wï¿½Sï¿½ï¿½ï¿½Zï¿½ï¿½x"Bï¿½ï¿½ï¿½Î[email protected]ï¿½æµ¦ï¿½ï¿½ï¿½ZZZZ[[%ï¿½ï¿½ï¿½Û¶mï¿½Ν;wï¿½Ú¥(49ï¿½Iï¿½ï¿½Dï¿½ &ï¿½.ï¿½Iï¿½"*jï¿½ï¿½Eï¿½ï¿½ï¿½...^Xï¿½~1/2<ï¿½ï¿½"w?ï¿½ï¿½Sï¿½_}WWï¿½ï¿½Ååª[ï¿½ï¿½ï¿½ï¿½lï¿½ï¿½BØH1ï¿½<ï¿½ï¿½ï¿½vï¿½ï¿½"ï¿½ï¿½ï¿½kM1aï¿½ï¿½XLï¿½ ï¿½oï¿½3/4}ï¿½ï¿½ï¿½.ï¿½ï¿½[!ï¿½ï¿½y "Sï¿½1/4uï¿½ï¿½ï¿½ï¿½ï¿½|>13/4Hï¿½ï¿½!0/IQWWwï¿½ï¿½7ï¿½}ï¿½ï¿½ï¿½ï¿½ï¿½hï¿½ï¿½ï¿½ï¿½ï¿½R"ï¿½ï¿½ï¿½ï¿½'Y"-cs ï¿½|ï¿½ï¿½'Ü¶Rï¿½Øï¿½kHï¿½@`^'â¡-zï¿½ï¿½-ï¿½vï¿½ï¿½wÞ{ï¿½r9ï¿½ï¿½(aEYï¿½- ï¿½-\Yï¿½Bï¿½(tm)c"'ï¿½ï¿½{.ï¿½ï¿½[ï¿½4ï¿½(r)ï¿½\$ï¿½9ï¿½-ï¿½ï¿½ï¿½1/2^ï¿½wï¿½ï¿½ï¿½3ï¿½ï¿½1/4cï¿½Æï¿½ï¿½ï¿½7ï¿½[ï¿½l'ï¿½@[email protected]ï¿½jï¿½ ï¿½4ï¿½Ïï¿½ï¿½Gï¿½Xayï¿½ï¿½ ï¿½ï¿½.ï¿½V-ï¿½. ï¿½ï¿½ï¿½|%ï¿½ï¿½ï¿½Gssï¿½kï¿½%ï¿½ï¿½ï¿½ï¿½0*ï¿½ï¿½ï¿½"yï¿½ï¿½2ï¿½5ï¿½Bï¿½Vï¿½Tï¿½Øï¿½ï¿½k /T4Oï¿½* T-ï¿½1/4ï¿½>nï¿½ï¿½vXOï¿½:uï¿½3/4ï¿½ï¿½"ï¿½qï¿½=ï¿½ï¿½Ø±ï¿½cÕªUï¿½[aï¿½ï¿½\~0ï¿½Nï¿½ï¿½ Wï¿½ï¿½Mï¿½"6 ï¿½a(tm)H`:ï¿½ï¿½% ï¿½ï¿½@ 1/2ï¿½ï¿½ï¿½ï¿½x<ï¿½H' "[...ï¿½Ûï¿½ï¿½(r)ï¿½ï¿½ï¿½3/4ï¿½ï¿½]ï¿½eï¿½!XU ï¿½sï¿½Lï¿½ï¿½-ï¿½"]Þï¿½A Ò¿ï¿½jIï¿½S]ï¿½ï¿½Nï¿½ï¿½u ï¿½i"?ï¿½ï¿½ï¿½yï¿½ï¿½- ï¿½"@O1ï¿½Ýï¿½ï¿½ï¿½År#ï¿½ï¿½ï¿½ï¿½5ï¿½ZAjï¿½bOH`Jz'<\ï¿½cMï¿½ï¿½ï¿½ï¿½JK6Pï¿½9ï¿½ï¿½Jï¿½'ï¿½ï¿½\$..."ï¿½Vï¿½ï¿½"ï¿½&

2. ## matrix power

only drawback is the length of the decimal numbers as opposed to a well-rounded whole number.

1. ## Math IA - Matrix Binomials

For (X+Y)n, where n=1, i.e. (X+Y): (X+Y)= = = =2I Where n=2, i.e. (X+Y)2: (X+Y)2=(X+Y)(X+Y) (X+Y)2= = = = =4I Where n=3, i.e. (X+Y)3: (X+Y)3=(X+Y)(X+Y)(X+Y) (X+Y)3=(X+Y)2(X+Y) (X+Y)3= = = = =8I Where n=4, i.e. (X+Y)4: (X+Y)4=(X+Y)(X+Y)(X+Y)(X+Y) (X+Y)4=(X+Y)3(X+Y) (X+Y)4= = = = =16I We can now find an expression for (X+Y)n through consideration of the integer powers of (X+Y)

2. ## Population trends in China

This model was introduced in the first cell and dragged down so that all cells followed the same rule. Model 554.8 603.5889 656.6682 714.4153 777.2407 845.5909 919.9517 1000.852 1088.866 1184.621 Model =554.8*(1.017^B2) =554.8*(1.017^B3) =554.8*(1.017^B4) =554.8*(1.017^B5) =554.8*(1.017^B6) =554.8*(1.017^B7) =554.8*(1.017^B8) =554.8*(1.017^B9) =554.8*(1.017^B10)

1. ## Modelling Probabilities in Games of Tennis

When we graph the data we get a histogram like the one on the next page: c) To find the expected value and standard deviation we must use the following equations: We have that n=10 and p= , so This information tells us that Adam usually wins 7 points, although

2. ## Modelling Probabilities on games of tennis

After finding the different ways the game can be played in, now I shall work out the probability of Adam winning the game. The different possible ways in which Adam can win the game are 4-0, 4-1, 4-2 and 4-3; and so now I will have to find the sum of probability of these events taking place.

1. ## The purpose of this investigation is to explore the various properties and concepts of ...

The scramble matrix is then multiplied by each packet of code and an encoded message is achieved. After encoding the message, instructions for decoding the message must be prepared. Using matrix algebra, a method of decoding is given to the partner along with other required information such as the cipher shift, scramble matrix and alphanumeric system.

2. ## Investigating Slopes Assessment

Tangent Gradient X= -2 Y= 24x+32 24 X= -1 Y= 6x+4 6 X= 0 Y= 0 0 X= 1 Y= 6x+(-4) 6 X= 2 Y= 24x+(-32) 24 1. For this one, after looking at the gradient, I realise that the function is similar to the results I found for A, however, this time the gradient is double.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to