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
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.
Middle
)2= 
2
= 
B3= (bY)3= (3)3
= 3
= 
B4= (bY)4= (3)4
= 4
= 
To test the above statement with a negative figure, Let “b” = (-3).
B2= (bY)2= (-3)2
= 
2
=
B3= (bY)3= (-3)3
= 3
= 
B4= (bY)4= (-3)4
= 4
=
Therefore we can assume that the formula Bn=bn×Yn-1 works in this case as well.
B2= b2xY2-1=
= 32x
= 9
=
B3= b3xY3-1=
= 33x
= 27
=
B4= b4xY4-1=
= 34x
= 81
=
B2= b2xY2-1=
= (-3)2x = 9
=
B3= b3xY3-1=
= (-3)3x =
(-27)=
B4= b4xY4-1=
= (-3)4x
= 81=
Decimals will be used for “b” in the following two examples.
B2=b2×Y2-1
= (0.5)2×Y1
= 0.25×
= 0.25
= 
B3=b3×Y3-1 = (0.5)3×Y2
= 0.125
= 0.125
=
B4=b4×Y4-1 = (0.5)4×Y3
= 0.0625×
= 0.0625
=
B2=b2×Y2-1 = (0.25)2×Y1
= 0.0625×
= 0.0625
= 
B3=b3×Y3-1 = (0.25)3×Y2
= 0.015625×
= 0.015625
= 
B4=b4×Y4-1 = (0.25)4×Y3
= 
×
= 
= 
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 “
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.
...read more.
Page
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