A series of extra rehearsals commenced in April. Each week participants could choose extra dancing rehearsals or extra singing rehearsals.
A matrix equation used to determine the number of students expected to attend these extra rehearsals is given by
`L_(n + 1) = [(0.85,0.25),(0.15,0.75)] xx L_n - [(5),(7)]`
where `L_n` is the column matrix that lists the number of students attending in week `n`.
The attendance matrix for the first week of extra rehearsals is given by
`L_1 = [(95),(97)]{:(text(dancing)),(text(singing)):}`
- Calculate the number of students who are expected to attend the extra singing rehearsals in week 3. (1 mark)
- Of the students who attended extra rehearsals in week 3, how many are not expected to return for any extra rehearsals in week 4? (1 mark)