"Let M = \begin{pmatrix}2&2\\ -4&8\end{pmatrix}
Find formulas for the entries of M^n, where n is a positive integer."
So I think this problem involves multiplying a matrix by itself continuously. But I do not think I have observed a link between the older entries and the newer entries each time I have multiplied this matrix by itself. It just seems to be random changes in the numbers (unless I am doing something wrong). Am I supposed to create a sequence out of each of the entries and then derive a general formula?
Also, I have managed to find the eigenvalues (4 and 6) and eigenvectors, but I am not too sure if they are relevant here. If they are relevant, how exactly would I apply them here?
Any assistance would be highly appreciated!
Find formulas for the entries of M^n, where n is a positive integer."
So I think this problem involves multiplying a matrix by itself continuously. But I do not think I have observed a link between the older entries and the newer entries each time I have multiplied this matrix by itself. It just seems to be random changes in the numbers (unless I am doing something wrong). Am I supposed to create a sequence out of each of the entries and then derive a general formula?
Also, I have managed to find the eigenvalues (4 and 6) and eigenvectors, but I am not too sure if they are relevant here. If they are relevant, how exactly would I apply them here?
Any assistance would be highly appreciated!
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