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Hi, I need help finding an equation for \(\begin{pmatrix} -4 & -15 \\ 2 & 7 \end{pmatrix}^n\). I've already found a pattern within this, but I don't know how to actually set it up so it works for all values. The top left value subtracts 10*(n-1) but it's only from its last value. For example, it can go from -34 to -74 from the third to fourth power. The top right value subtracts 30, then 60, then 120 etc. The bottom left value adds in powers of two, from the last value as well. So it could go from 6 to 14 to 30 (+8 then +16). Bottom right is the same thing but only in multiples fo 12 multiplied by two. It could go as 19 to 43 to 91 (+ 24 then +48). I think the problem I'm having problems with is how to incorporate the last values it had before. This is also made tough because this is for all real numbers

 Oct 18, 2020
edited by Guest  Oct 18, 2020

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