# Maths Portfolio Matrix Binomials

Maths Portfolio

SL Type 1

Matrix Binomials

In this mathematics portfolio we are instructed to investigate matrix binomials and algebraically find a general statement that combines perfectly with our matrices and equations given.

MATRIX BINOMIALS

Given that:

and

We calculated

Therefore:

And

We were then requested to find expressions for

by considering the integer powers of X and Y:

These expressions were found by observing that the result of was always the matrix to the power of n multiplied by 2 to the power of n-1. The sequence of results gives us: 1, 2, 4 and 8, reaffirming our expressions are correct because .

Given that:

and  where a and b are constants

We were asked to find using different values of a and b and then find the expressions for .

Therefore:

And:

Assuming that a = 2

Assuming that a = 3

Assuming that a = 6

Assuming that a = -4

Assuming that b = -1

Assuming that b = 4

Assuming that b = 5

Assuming that b = 7

To ...