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. These constants will lead to the development of the general statement. Basic matrices skills will help to develop to multiply, add, and develop formulas. Different matrix scenarios will be used to verifying that statements and formulas are true. In the different scenarios, values of constants will be manipulated to find any limitations in the final general statement. The end result will be a general statement that satisfies the rules of matrices and proves their relationship.

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Determining X and Y

Since we know that X=  and Y=, we can therefore assume that any of these matrices multiplied by themselves will give increasing exponential results.

Throughout the assignment, bolded matrices are expanded form of the original equation, and blue matrices are the final answer.

X2 =  x

=

X3 = X2 =

=

X4 = X3 =

=

Since we know that X multiplied by X = X2  and X2 times X = X3, we can assume that matrix Xn multiplied by the original matrix ...

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