I'm preparing or my exam in linear algebra and I'm stuck with a question. I've tried to find some help in my textbook (Linear Algebra and its applications, 4th Edition, By David C. Lay). I can't find anything about it (maybe because the question is written in danish and I'm having trouble translating it right?).
I'm asked to find the limiting value, $\lim_{n \to \infty}A^nx$ where
$ A = \begin{bmatrix} 0.25 & -0.75 & 0.75 \\[0.3em] -0.5 & 0 & 0.5 \\[0.3em] 0.25 & -0.25 & 0.75 \end{bmatrix} $ $ x = \begin{bmatrix} 2 \\[0.3em] 3 \\[0.3em] 3 \end{bmatrix} $
How am I supposed to solve this? I'm not asking you to calculate the answer for me, but I'm asking for the right way to solve this kind of problem.