find the steady state of : Matrix attached. Please help

Question

anonymous · Answer

|3/5   1/6|
|2/5    5/6|

amistre64 · Answer

steady state is when input no longer affects the outcome right?

anonymous · Answer

yes

anonymous · Answer

I am dealing with diagonal matrix, eigenvector, M^infinitive and steady state.

amistre64 · Answer

so we require a vector x  such that Ax = x

let x^T = [a b]

3a/5  +    b/6 = 0
2a/5  +  5b/6 = 0

looks to be a start

anonymous · Answer

sorry, D, not P^-1. and from now, my nightmare starts

anonymous · Answer

It took me long time to get D = $$\left[\begin{matrix}1 & 0 \ 0 & -13/30\end{matrix}\right]$$

anonymous · Answer

and how to get M^n is another sky to me. I appreciate that someone can check my stuff and show me what is wrong with mine.

amistre64 · Answer

its been awhile since i had to worry about the specifics, but ill have time to look over your process either later today or tomorrow

anonymous · Answer

thanks a lot. I don't want to just jump into the formula and skip the steps. I know the steady state must be the same with eigenvalue, but how? stop at eigenvalue 1, figure out its eigenvector and then , put it into the formula  is easiest way to get the right answer. I don't like it when I cannot perform mathematic baby skill in calculating the matrix. shame on myself.