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Matrices and vectors are introduced as a linear algebra formalism to make manipulations and calculations simpler when studying a Markov chain, especially for iterating states efficiently over many steps.

Conditions: The problem involves a Markov chain.; The goal is to compute future states or manipulate transition probabilities.

Matrices and vectors are introduced as a linear algebra formalism to make manipulations and calculations simpler when studying a Markov chain, especially for iterating states efficiently over many steps.

Conditions: The problem involves a Markov chain.; The goal is to compute future states or manipulate transition probabilities.