Construct the Markov diagram for this game and show that the associate transition matrix T can be written as the following. Show that λ = 1 is an eigenvalue of T. If can answer both (a)and(b), else answer (b). In a simplified version of a popular online game, a team of Champions move between locationsto protect their own Nexus, whilst attempting to destroy the opponent team's Nexus. We knowthe following about the locations and rules for movement:• A team consists of 5 Champions• There are five locations: Home (Nexus),Enemy (Nexus), Safe lane, Mid lane, and Off lane.• Home is adjacent to the Safe lane, Mid lane, and Off lane• Enemy is adjacent to the Safe lane, Mid lane, and Off lane• No other connections exist• All connections are bi-directional (Champions can move in both directions)• For safety reasons, Champions must move to an adjacent location at each time step andcannot stay in the same location• Champions move to adjacent locations with equal probabilities at each time step andcannot stay in the same location.If you wish, you can simplify the location using their respective starting letters. I.e. H,E,S,M,0.Stylistic note: If you have a strong preference, you may use Ancient/Hero in place of Nexus/Champion.(a) Construct the Markov diagram for this game and show that the associate transition matrixT can be written as the following.11T =0 0Hint: Be sure to state your ordering of the states and justify the entries in T(b) Show that A= 1 is an eigenvalue of THINHIN O OO O H1 313O O 1/3H3113

In the given question, we are asked to show that the eigenvalue λ=1 is an eigenvalue of the matrix…

Answered: T= 00 3 w|wo|wo|TOO 3 1|21|20 H2H2OOO…

T= 00 3 w|wo|wo|TOO 3 1|21|20 H2H2OOO 1|21|200 00 00 0 0 Hint: Be sure to state your ordering of the states and justify the entries in T Show that X = 1 is an eigenvalue of T

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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