Unsure if my attempt is correct, pasted the information below
Problem entails a Markov transition matrix worded question which I find a little tricky.
Problem + my attempt https://imgur.com/a/Nxl8l9f
2026-03-27 21:23:29.1774646609
Determining Markov transition matrix
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Going with a pedestrian approach: A letter is followed by another letter with probability 0.8. If it is a vowel, it is followed by a consonant with probability 0.64 (0.8*0.8) overall. If it is a consonant, it is followed by a vowel with probability 0.4 overall. So we already have $$ P(V,C) = 0.64, P(V,V) = 0.16, P(C, V) = 0.4, P(C,C) = 0.4, $$ which corresponds to your first 4 values. Since $0.2*0.9 = 0.18$ this is the probability for a letter to be followed by a blank space. Hence it remains a probability $0.02$ to be followed by a punctuation mark. The last hypotheses gives exacty what you have.
Remember that one of the easiest thing to check when you are writting a transition matrix as this one is that the sum of each line must be equal to one (starting from anywhere, we must go somewhere). On the other hand there is no requisite on the sum of each column.