(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I'm fine on part a), and for part b) I got 0.162 and c) I got 1/9, 2/9 and 0.481, although didn't feel too sure about those.

I'm stuck on part d).

The eigenvalues are

1

0.8734

-0.0799 + 0.1101i

-0.0799 - 0.1101i

0.5

0.2865

And eigenvectors are

[0] ..... [-0.1269] ..... [-0.6328] .................. [-0.6328]

[0] ..... [-0.0832] ..... [ 0.3823 + 0.3589i] ..... [ 0.3823 - 0.3589i]

[0] ..... [-0.0991] ..... [ 0.4630 - 0.2784i] ..... [ 0.4630 + 0.2784i]

[0] ..... [-0.1380] ..... [-0.0547 - 0.0335i] ..... [-0.0547 + 0.0335i]

[0] ..... [-0.4276] ..... [-0.1049 - 0.1061i] ..... [-0.1049 + 0.1061i]

[1] ..... [ 0.8748] ..... [-0.0529 + 0.0591i] ..... [-0.0529 - 0.0591i]

[ 0] ............. [-0.1637]

[ 0] ............. [ 0.3793]

[ 0] ............. [ 0.6000]

[ 0.7071] ..... [-0.6365]

[-0.7071] ..... [-0.2447]

[ 0] ............. [ 0.0657]

But I don't really know what to do from here. I know 0 < μ < 1, and I'm guessing there might be a way to write x(0) in a linear combination of the eigenvectors, but don't see how this will help. Sorry for the rubbish formatting.

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# Markov chains, probability.

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