| Age\Severity | Slight | Mild | Severe |
| 0 - 30 | 0.5 | 0.3 | 0.2 |
| 30 - 60 | 0.4 | 0.3 | 0.3 |
| 60 - 90 | 0.1 | 0.4 | 0.5 |
We can represent the table by the mat ix
\[\left( \begin{array}{ccc} 0.5 & 0.3 & 0.2 \\ 0.4 & 0.3 & 0.3 \\ 0.1 & 0.4 & 0.5 \end{array} \right)\]
, the the people above by the vector \[\begin{pmatrix}300\\500\\200\end{pmatrix}\]
.\[\left( \begin{array}{ccc} 0.5 & 0.3 & 0.2 \\ 0.4 & 0.3 & 0.3 \\ 0.1 & 0.4 & 0.5 \end{array} \right)\begin{pmatrix}300\\500\\200\end{pmatrix}= \begin{pmatrix}370\\320\\310\end{pmatrix}\]
370 people have a slight form of the disease, 320 have a mild form of the disease, and 310 have a severe form of the disease.