November 1st, 2017, 04:12 PM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1  Power Formula
Power Formula for A=$\begin{pmatrix} \Lambda & 1 & 0\\ 0 & \Lambda & 1\\ 0 & 0 & 1 \end{pmatrix}^n$
Last edited by ZMD; November 1st, 2017 at 04:16 PM. 
November 1st, 2017, 04:41 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,888 Thanks: 765 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle A^n = \left ( \begin{matrix} \Lambda ^n & n \Lambda ^{n  1} & 1 + 2 \Lambda + \dots + (n  1) \Lambda ^{n  2} \\ 0 & \Lambda ^n & 1 + \Lambda + \Lambda ^2 + \dots + \Lambda ^{n  1} \\ 0 & 0 & 1 \end{matrix} \right )$ You can use induction to prove this formula. Did that answer your question? Dan  

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