Show that λ = 1 is an eigenvalue of T. Answer (b) only. 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 adiacent 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,O.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.T =0 03Hint: 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 11333

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Answered: Show that λ = 1 is an eigenvalue of T.…

Show that λ = 1 is an eigenvalue of T. Answer (b) only.

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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