# In this portfolio,my assignment is to deal with matrix binomials,and to investigate them.

PORTFOLIO TYPE I – MATHEMATICAL INVESTIGATION

-MATRIX BINOMIALS-

Student: Domazet Neven SL

In this portfolio,my assignment is to deal with matrix binomials,and to investigate them.

At first,my initial matrices are as follows:

and

Now,my task is to find and calculate following matrices: : X2, X3, X4; Y2,Y3 and Y4

So,since  and  we will calculate that as

We know that we can express multiplication of matrices as ,and it goes like

,so we get that , thus.  Or 2* =2* X

As we now know this,it is easy to calculate ,because or 2*X*X,which is 2*2*X or it is equal to 22*X and equal to .

is defined as X3*X=22 *X*X=22 *2*X=23 *X and our solution is =

Procedure for Y is completely the same as for X,and we do not have to go in details,so to calculate the products of , and , we will use the TI-84 Plus Texas Instruments Graphic Calculator and obtain the results in the following form ( [B] equals Y)

The results are as follows: ;  and .

Now to continue with our work we need our previous results,because they can help us to find ,  and .Results are shown in table below

Here we can see some characteristics which can help us in our work,and we will stick to them,and applying the rule to the results we will get the following matrix identities:

;      ;       ;     .

If we express every coefficient as ,we get  ;   ;   ; .

Next table that can help us is the one  dealing with relation between the powers

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