Use probability matrix for changes from sunny, cloudy, and rainy days. Assume that the initial probability distribution for a sunny, cloudy, or rainy day is not a single state, but some combination of the 3 states.

If the relative probability of a sunny, cloudy, or rainy day after 4 days is (0.4382, 0.2362, 0.3256), what was the state on day 0? Use a matrix inverse to work backwards.

Answer: (0.9, 0.1, 0.0).

Please show step-by-step work.