# Matrix power. The internal assessment will focused on observing patterns of matrix powers which will be the main key to find the general expression of matrix powers.

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Introduction

Internal Assessment- Matrix Powers

The internal assessment will focused on observing patterns of matrix powers which will be the main key to find the general expression of matrix powers.

1)

Explanation: When matrix M is powered by 2 it gives a result offrom GDC, when M is powered by 3 it gives a result of from GDC and when M is powered by 4 it gives a result of from GDC. The pattern shown is that every time M is powered by a number after its preceding number it is multiply by 2. For instance, 4 shown in matrix, 8 shown in matrix, and 16 shown in matrix . Thus, these results make a general expression that. This formula is proven correct because when

Middle

Explanation: When matrix S is powered by 3 it gives a result of from GDC, when matrix S is powered by 4 it gives a result offrom GDC, and when matrix S is powered by 5 it gives a result of from GDC. The pattern shown is that results have a common factor of such as 4 shown in matrix, 8 shown in matrix, and then16 shown in matrix. Once the resulting matrix is factor out, the

Conclusion

4)

Explanation: After a further investigation with further values of k and n, the results shows that the limitation for n is that all negative numbers and non-integers value because when a matrix is powered by negative numbers or non-integers value the calculator gives a math error text. In addition there’s no limitation for k.

5)

In conclusion,

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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