For this problem you will need to use the commands you learned for finding eigenvalues and eigenvectors on the webpage that was linked in the introduction of the project. There is a cell for you to enter these with Sage, and you will screenshot that with the problem to paste to your project.

You can answer the rest of the parts of the question with whichever method you prefer and type your answers onto your project that you will submit

These are the only two problems for this project, so when you are done with this question, save and submit as you did with the first two projects.

Consider the stochastic matrix:

A equals open square brackets table row $1$ cell $0\mathrm{.}3$ end cell cell $0\mathrm{.}1$ end cell row $0$ cell $0\mathrm{.}4$ end cell cell $0\mathrm{.}1$ end cell row $0$ cell $0\mathrm{.}3$ end cell cell $0\mathrm{.}8$ end cell end table close square brackets

a$.$ Use the Sage coding box below to compute the eigenvalues and eigenvectors for the matrix.

b$.$ Find the steady state vectors of A$.$

c$.$ Are there any generalizations that can be made about the long$-$term behavior of a Markov chain defined by A$?$ If so$,$ what?