import numpy as npimport numpy.linalg as ladef steady$\_$state$\_$vector$($mat$)$: dimension $=$ mat.shape$[0]$ # Store the dimension of the matrix mat$2=$ mat $-$ np$.$eye$($dimension$)$ # mat$2$ is mat $-$ Identity Matrix $($I$)$ ones $=$ np$.$ones$($dimension$)$ mat$2=$ np$.$c$\_[$mat$2,$ ones$]$ X $=$ np$.$dot$($mat$2,$ mat$2.$T$)$ Y $=$ np$.$ones$($dimension$)$ return la$.$solve$($X$,$ Y$)$def three$\_$step$\_$transition$($mat$,$ i$,$ j$)$: temp $=$ mat # Initialize temp with mat$^1$ temp $=$ np$.$dot$($temp$,$ mat$)$ # Calculate temp$^2$ temp $=$ np$.$dot$($temp$,$ mat$)$ # Calculate temp$^3$ return temp$[$i$][$j$]$markov$\_$matrix $=$ np$.$array$([[0\mathrm{.}8,0\mathrm{.}05,0\mathrm{.}01,0\mathrm{.}14],[0\mathrm{.}1,0\mathrm{.}4,0\mathrm{.}1,0\mathrm{.}4],[0\mathrm{.}1,0\mathrm{.}05,0\mathrm{.}7,0\mathrm{.}15],[0\mathrm{.}1,0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}75]])$steady$\_$state $=$ steady$\_$state$\_$vector$($markov$\_$matrix$)$prob$\_$stark $=$ three$\_$step$\_$transition$($markov$\_$matrix, $0,1)$ # $0-$ House Targaryen, $1-$ House Stark# Print the resultsprint$("$Steady State Vector:"$)$print$($steady$\_$state$)$print$("$Probability of Transition from House Targaryen to House Stark after $3$ steps:"$)$print$($prob$\_$stark$)$