Tut 3 Q3.6 (Attached).

I'm trying to solve this like 3.5 but my issue is that equations 3 and 4 are inconsistent because of the repeated eigenvalue so how do I go about this?

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Your issue can be resolved by referring to the hint given in the question. The diagonalisation method only leads to a general formula for the transition probabilities for n>0, due to the zero eigenvalue. As a result, equations 1 and 3 in your answer are irrelevant. You can then notice that the formulae for the transition probabilities are simply constant for n>0.