Exercise $7\mathrm{.}3\mathrm{.}5$ The following is a Markov $($migration$)$ matrix for three locations $511552$

$221555$

$222555$

$($a$)$ Initially, there are $130$ individuals in location $1,300$ in location $2,$ and $70$ in location $3.$ How many are in each location after two time periods?

$($b$)$ The total number of individuals in the migration process is $500.$ After a long time, how many are in each location?