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Let P be a 2 x 2 stochastic matrix. Prove that there exists a 2 x...

Let P be a 2 x 2 stochastic matrix. Prove that there exists a 2 x 1 state matrix X with nonnegative entries such that P X = X. Hint: First prove that there exists X. I then proved that x1 and x2 had to be the same sign to finish off the proof

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