 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof/1/a/solution

The transition matrix acts on a column probability vector in the order Central, Headington, Botley. Thus column

j

records the destinations of buses starting at station

j

. The Central-to-Headington, Headington-to-Botley and Botley-to-Central entries give

A = B = C = 0.1, P = 0.6 0.1 0.3 0.1 0.8 0.1 0.1 0.2 0.7 .

Each column sums to one, as required for this column convention for a stochastic matrix.

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