# Matrix Binomials t2

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.

The term "matrix" was thought up by some very famous mathematicians such as . , , ,  and  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.

From these calculations we can easily state that there is a pattern within the results of the variations of and when there is an increase in the power of the matrix. I can clearly state that there is a relationship between the power of the matrix and the end product of the matrices.

For both the variables we get the same results except for the negative signs that represent inverse matrices depending on the initial matrix. But they always take upon the same position so it doesn’t influence our answers. Through these results I see that a way to find a general statement for both and I could use my knowledge of sequences and series along with that of matrices.

Considering integer powers of and, we can find expressions for.

Looking at both the matrices values, I realized that we were dealing with geometric sequences. Before following up with these I can ...