so I’m trying to find the steady state of this matrix but it’s not a Markov chain. It’s for the second problem on the picture to find what predatory value makes both populations stable. Through trial and error I figured out p=.16 for the matrix to converge to a stable population but I don’t know how to do it other than trial and error. My professor said in class to find the steady state of the matrix but I thought you could only do that if it was a markov chain? (https://i.stack.imgur.com/KrgAp.jpg)
2026-03-29 18:17:38.1774808258
How to find steady predator/prey matrix
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Once we've reached the steady state $X$, we want $AX=X$, so $X$ is an eigenvector of $A$ with eigenvalue $1$. Therefore, we must choose $p$ so that $A$ has an eigenvalue of $1$.
Can you take it from here?