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Properties of Transition Matrices
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I. The transition matrix $$T=\begin{pmatrix}0.7 & 0.2 \\ 0.3 & 0.8\end{pmatrix}$$ has columns that each sum to 1.

II. Transition matrices are utilized to model dynamic systems over discrete time intervals.

III. The inverse of a transition matrix always exists.

Which of these statements regarding the transition matrix $$T$$ are true?

Transition Matrix T: $$\begin{pmatrix}0.7 & 0.2 \\ 0.3 & 0.8\end{pmatrix}$$

A

Only statement I is true.

B

Only statements I and II are true.

C

All statements I, II, and III are true.

D

Only statements II and III are true.

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