• 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
  17. 17
    17
  18. 18
    18
  19. 19
    19

Math Type I SL Matrices

Extracts from this document...

Introduction

Pure 20 IB Portfolio Project

Matrix Binomials

Dan Stoica

Henry Wise Wood High School

Calgary, Alberta

Mr. Bedford

Table of Contents

Title Page...........................................................................................................Page 1

Table of Contents............................................................................................Page 2

Mathematical Investigation Sheet...........................................................Page 3

Calculator/Introduction..............................................................................Page 4

Determining X and Y.....................................................................................Page 5

Determining X and Y continued...............................................................Page 6

Determining A and B.....................................................................................Page 7

Determining A and B continued...............................................................Page 8

Determining A and B continued...............................................................Page 9

Determining A and B continued............................................................Page 10

Determining A and B continued............................................................Page 11

Determining Expressions for (A + B)..................................................Page 12

Verifying (M).................................................................................................Page 13

Verifying (M) continued...........................................................................Page 14

Verifying (M) continued...........................................................................Page 15

Verifying (M) continued...........................................................................Page 16

Conclusion......................................................................................................Page 17

Mathematical Investigation Question

image00.jpg

Ti-84 Calculator Matrix Skills

How to enter a matrix

2nd  MATH -> Edit -> Choose “Letter” -> Enter Dimensions -> Enter Values

How to select a matrix

2nd MATH -> Select “Letter”

How to perform operations on matrices

2nd MATH -> Select Matrix -> Operation Key(+,-,*,/,) -> 2nd -> Select another Matrix -> Enter

How to put exponents on a matrix

2nd MATH -> Select Matrix -> Press ^ -> Press Number desired as exponent -> Enter

Introduction

        In the proceeding project, 2 by 2 matrices will be used to create a general statement. Different values will be used for constants and exponents.

...read more.

Middle

image17.png)2

= image18.pngimage18.png2

= image19.pngimage19.png

B3= (bY)3= (3image17.pngimage17.png)3

= image18.pngimage18.png3

= image20.pngimage20.png

B4= (bY)4= (3image17.pngimage17.png)4

= image18.pngimage18.png4

= image21.pngimage21.png

To test the above statement with a negative figure, Let “b” = (-3).

B2= (bY)2= (-3image17.pngimage17.png)2

= image22.pngimage22.png2

= image19.pngimage19.png

B3= (bY)3= (-3image17.pngimage17.png)3

= image22.pngimage22.png3

= image24.pngimage24.png

B4= (bY)4= (-3image17.pngimage17.png)4

= image22.pngimage22.png4

= image21.pngimage21.png

Therefore we can assume that the formula Bn=bn×Yn-1image17.pngimage17.png works in this case as well.

B2= b2xY2-1image17.pngimage17.png=

= 32ximage25.pngimage25.png = 9image26.pngimage26.png

= image19.pngimage19.png

B3= b3xY3-1image17.pngimage17.png=

= 33ximage28.pngimage28.png = 27image29.pngimage29.png

= image20.pngimage20.png

B4= b4xY4-1image17.pngimage17.png=

= 34ximage30.pngimage30.png = 81image31.pngimage31.png

= image21.pngimage21.png

B2= b2xY2-1image17.pngimage17.png=

= (-3)2ximage25.pngimage25.png = 9image26.pngimage26.png

= image19.pngimage19.png

B3= b3xY3-1image17.pngimage17.png=

= (-3)3ximage28.pngimage28.png =

(-27)image29.pngimage29.png= image24.pngimage24.png

B4= b4xY4-1image17.pngimage17.png=

= (-3)4ximage33.pngimage33.png = 81image26.pngimage26.png= image21.pngimage21.png

Decimals will be used for “b” in the following two examples.

B2=b2×Y2-1image34.pngimage34.png = (0.5)2×Y1image17.pngimage17.png

= 0.25×image25.pngimage25.png

= 0.25image26.pngimage26.png

= image35.pngimage35.png

B3=b3×Y3-1image34.pngimage34.png = (0.5)3×Y2image17.pngimage17.png

= 0.125image28.pngimage28.png

= 0.125image29.pngimage29.png

= image35.pngimage35.png

B4=b4×Y4-1image34.pngimage34.png = (0.5)4×Y3image17.pngimage17.png

= 0.0625×image30.pngimage30.png

= 0.0625image31.pngimage31.png

= image35.pngimage35.png

B2=b2×Y2-1image34.pngimage34.png = (0.25)2×Y1image17.pngimage17.png

= 0.0625×image25.pngimage25.png

= 0.0625image26.pngimage26.png

= image36.pngimage36.png

B3=b3×Y3-1image34.pngimage34.png = (0.25)3×Y2image17.pngimage17.png

= 0.015625×image28.pngimage28.png

= 0.015625image29.pngimage29.png

= image38.pngimage38.png

B4=b4×Y4-1image34.pngimage34.png = (0.25)4×Y3image17.pngimage17.png

= image39.pngimage39.png×image30.pngimage30.png

= image40.pngimage40.png

= image41.pngimage41.png

Therefore we can conclude that the formula Bn=bnYn works. From these examples, we can conclude that this statement works with positive, negative, and decimals for the “b” figure, just as it did for “a” when tested above. There are no limitations to this statement. Therefore, the statement is valid. A also check the answers using the matrix feature on the TI-84 calculator.

Patterns that were observed during this test were that whenever “

...read more.

Conclusion

Mn = anXn+bnYnis valid, and can be proved by using other expressions and by using examples, and provides answers that are consistent, that make sense, and that are logical.

Page

...read more.

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

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    Þ��pL�"e U(�/� ����NBP3-�=�]�Ô5#!�",|�/�1/4��?"�-�>�o}�h�I� � k�x�0z����m�iQ-�.�...h�ԧ&(r)� /`��.�-�$6���S_6r� �t���'"t<�$�T"�����Y��F �m�K^�_x�//H P� H��T�'��E��|�ʸ'�|9�""�kSD<8s�z�8tv����{c��0��� ]i'�?6�3R��0�"Zr�fɪ�Ö��n����z�' }A(r) P-p�Od^��=�C'�"�,j�n�1@""k�Hw{}x �v':L*�3/4��F�&@�f'�mr�>�m"���C����@Z�"�zI5' ��(tm)b�r}Í¿cw��x�A3/41/2+���dé¤D��(�x��Q���N�(LR.qf�?Ë£}��d�����4ß²'"F_��x�(c)��6'q ��\�S��BK$���B�1���(�-��% �N-È¿ Æ°T*��!�P�Ú?q���Z��XG*�.Ұ�E:ES5����7C�]_�D=�}(tm)z"��\b'1/2k'�H&'��d�j���J���XLJ`U'-�3/4� ��d.���4}�i! # � �&�{:)_3��3��T`��Y�v�q�Ħa q�' D��S�ÎI��2k-��� r.�p"D���v#�-;���$-�(r Ù��:?�綸��8�����l��NI �5�7#8a��'�m �HϹa(r)7��Ln֬�m!8uj�(r)!�P X'}��=-1/4zzO� 6�1/2�"�~ �K -�(=q&�PE���~"�G(tm)�p' ����,wM-�ٹ�!���VY>��(2�צ4L�� ZO*J`�1/4I�',Á9�'f�\N�0#�$�ÄBÓ¥{b�h�C#߬'6�-'`K|�V�n����$R�|�"9L� O~<�u÷�È�6 SL*� $��k Za��(tm)Q2�d��8��?���0��ß�n��� P"�дzH`��F���U���c@�-���ެ_d1��^¿z�H(r)�l-"'h�5� !1��82|��?;�j%��f�F��3� �ei��!C�"� ���T�{#D�A��HT�5"��Sy(tm)���k*�Z��X��?Ä��2�U�v� �� � -�+YW��k���hWP�(r)_��<W 4<�"�E�uZ�+v��D ��-"��u� ;]���(� ��s`�Z��� z...�$��Y'��"8xY�'��*'R��<��j_H�M����%'

  2. IB math SL type 2 project

    Use TI Connect to graph and print each graph. (a) The container of CentiKeeper Company Graph 1: The Change of Temperature According to the Equation of y = 70+(200-70)e-0.016x (b) The Container of TempControl Company Graph 2: The Change of Temperature According to the Equation of y = 60+(200-60)e-0.017x (c)

  1. Math IB SL BMI Portfolio

    However, the second half of model, plotted using a logistic function, is still likely to fit the data after some changes to the variables. This is due to the theory behind why a logistic function is perfect in fitting data for "growth towards a fixed capacity".

  2. Math IA Type 1 In this task I will investigate the patterns in the ...

    Therefore the 2 intersections of the parabola with the first line[y=x] are: X1 = X4 = Now substituting values of x1, x2, x3, x4 into the formula: --> Therefore D = Even though this conjecture has been proven, still there are some limitations * The lines intersecting the function must be y = x and y = 2x.

  1. Math IA - Matrix Binomials

    Let A=aX, where a is a constant. Using different values of a, we can calculate A2, A3, A4: In order to ensure the validity of our findings, we will use 3 different values of a (2, -2, and 10). When a=2, i.e.

  2. IB Math Methods SL: Internal Assessment on Gold Medal Heights

    Let us attempt to discover what the height will be for the record in 1984; assuming that the functions remains true. Take a look at the graph below. Graph 6: Functions showing future heights based upon trends: 1984 However, there are flaws in this hypothetical argument.

  1. Math SL Fish Production IA

    ________________ The quartic model that was developed earlier does not fit the new data; it does not connect any of the points. The data points form a curve and the total mass seem to increase at a constant rate from the 1st year onwards.

  2. SL Math IA: Fishing Rods

    Second, I used the x values of 3 (in the first set) and 6 (in the second set) to once again allow for a broad representation of the data points in the final quadratic equation. Both of these points (3 and 6)

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