Q$5.$ Suppose three robots are executing the consensus algorithm over their $x-$

coordinates and are communicating via an $L_3$ graph. Assuming that at time $t_0$ the

initial values of their $x-$coordinates are $x_1(t_0),x_2(t_0)$ and $x_3(t_0)$; show with a

derivation what happens to their $x-$coordinates as time tends to infinity. $[12$ points$]$