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# matix bimonals

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Introduction

Mathematics Portfolio – Matrix Binomials                                                                                            Samed Nakhla

## Matrix Binomials

Question

1. Let  Solution      Question

1. By considering integer powers of X and Y, find expressions for  Following the pattern in the first question and noticing from it, I deduce that the formula for:  Also to find the  power of (X+Y) I will use some examples to find the pattern in it:   From the examples above, I deduced the equation of  by following the pattern, and it is: Question

Let A=aX and B=bY, where a and b

Middle

a and b

Let’s assume that a= 2   Also, let’s assume that b=3   To obtain the general formula for  we need to find a formula for  without using different values of a and b, are:      Question

By considering integer powers of A and B, find expressions for  Solution

By following the pattern in the previous question, one can deduce that the formulas are:  And to find the formula for  , one should give some examples

Conclusion

bY.

Solution

After following the pattern in the previous question, I concluded the formula of  to be: To obtain the general formula of  in terms of aX and bY: Question

Test the validity of your general statement by using different values of a, b and n.

Solution

Let’s assume that a=2, b=3 and n=3 And by using the formulas we got from before  Where  So, also by assuming the same variables as before a=2, b=3 and n=3, and then replacing them in the equation  , we get the exact result as before: This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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1. ## Matrix Binomials

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1. ## Matrix Binomials

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