To begin with, we assume that people live in either Alberta or BC. We represent a transition matrix as T=[ T i j {\displaystyle T_{ij}} ].
Then, T 11 = 0.9 {\displaystyle T_{11}=0.9} , T 12 = 0.15 {\displaystyle T_{12}=0.15} , T 21 = 0.1 {\displaystyle T_{21}=0.1} and finally T 22 = 0.85 {\displaystyle T_{22}=0.85} . Thus, we have T = [ 0.9 0.15 0.1 0.85 ] {\displaystyle T={\begin{bmatrix}0.9&0.15\\0.1&0.85\end{bmatrix}}} .