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I used the equation Sn=T^-1 (Sn+1 -F) to work backwards and find the previous month from a transition matrix, but my values end up being large numbers, as well as a negative value. How do I interpret these values from here?

Edit: These are the workings for further clarifications. I do not understand how to interpret these values, especially the negative result.

workings

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Without more details it's not clear what's going on here, but it's quite possible that your transition matrix is ill-conditioned. If so, you can't "interpret these values".

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