In a simplified version of a classic murder mystery board game, players move between locations to...

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In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: • There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. Dining Room is adjacent to Kitchen, Cellar, and Lounge • Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) • Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are adjacent (in addition to the above) • All connections are bi-directional (players can move in both directions) ● Players must move to an adjacent location on each turn and cannot stay in the same location Players move to adjacent locations with equal probabilities at each time step If you wish, you can simplify the location using their respective starting letters. I.e. K,B,D,C,L,H ● ● Prove (without computing powers of T) that the matrix T is not a regular matrix. In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: • There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. Dining Room is adjacent to Kitchen, Cellar, and Lounge • Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) • Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are adjacent (in addition to the above) • All connections are bi-directional (players can move in both directions) ● Players must move to an adjacent location on each turn and cannot stay in the same location Players move to adjacent locations with equal probabilities at each time step If you wish, you can simplify the location using their respective starting letters. I.e. K,B,D,C,L,H ● ● Prove (without computing powers of T) that the matrix T is not a regular matrix.

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To prove that the matrix T is not a regular matrix we must first understand what a regular matrix is ... View the full answer