This problem first appeared on another thread under Statistics and probability. I found it when I got the same problem, which is as follows(adsbygoogle = window.adsbygoogle || []).push({});

Consider matrices in the form (k+1 k-1)

(k-1 k+1)

We will call this matrix Mk, find a general expression for Mk to the nth power in terms of k and n.

I tried several different matrices of this form, the general expression i came up with is attached in the thumbnail, but I still tried making it somewhat clear with latex.

M[tex]^{N}_{K}[/tex] = 2[tex]^{n-1}[/tex][tex]\left( [(k+1) +(k - 1)\sum^{n}_{x=1} k^{x}] [(k-1) +(k - 1)\sum^{n}_{x=1} k^{x}] \right)[/tex]

[tex]\left([(k - 1) +(k - 1)\sum^{n}_{x=1} k^{x}] [(k + 1) +(k - 1)\sum^{n}_{x=1} k^{x}] \right)[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrix Powers

**Physics Forums | Science Articles, Homework Help, Discussion**