smc-1893-30-2×2 Matrix

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)

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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)

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a. `text(Using matrix equation,)`

`L_2`	`= T xx L_1-[(5),(7)]`
	`= [(0.85,0.25),(0.15,0.75)][(95),(97)]-[(5),(7)]= [(100),(80)]`

`L_3`

`= [(0.85,0.25),(0.15,0.75)][(100),(80)]-[(5),(7)]= [(100),(68)]`

`:.\ text(68 students are expected to attend singing in week 3.)`

`L_4`

`= [(0.85,0.25),(0.15,0.75)][(100),(68)]-[(5),(7)]= [(97),(59)]`

`:.\ text(Students expected not to return)`

`= (100 + 68)-(97 + 59)`

`= 12`

MATRICES, FUR2 2009 VCAA 4