An enrichment centre offers drama, writing and speech enrichment classes on weekdays during the school holiday. The matrix S shows the number of students who attend the different classes for beginners and advanced levels in a day. $S = \begin{pmatrix}25 & 32 & 40 \\ 21 & 19 & 32\end{pmatrix}$ Columns (in order): drama, writing, speech.
Rows (in order): beginners; advanced. The school fee for drama cost $40 per session, $25 per session for writing and $30 per session for speech. The fees for beginner and advanced learners are the same for each type of class.

1. Multiply every element of $S$ by 5

$W=5S=5\begin{pmatrix}25&32&40\\21&19&32\end{pmatrix}=\begin{pmatrix}5(25)&5(32)&5(40)\\5(21)&5(19)&5(32)\end{pmatrix}$
$W=\begin{pmatrix}125&160&200\\105&95&160\end{pmatrix}$

1. Write the class fees as a column matrix in the correct order

Fees per session:

Drama = $40, Writing = $25, Speech = $30.

Since the columns of $S$ are in the order drama, writing, speech,

$C=\begin{pmatrix}40\\25\\30\end{pmatrix}$

1. Set up the multiplication of the $2\times3$ matrix $W$ and the $3\times1$ matrix $C$

Using
$W=\begin{pmatrix}125&160&200\\105&95&160\end{pmatrix},\quad C=\begin{pmatrix}40\\25\\30\end{pmatrix},$
$T=WC=\begin{pmatrix}125&160&200\\105&95&160\end{pmatrix}\begin{pmatrix}40\\25\\30\end{pmatrix}.$

2. Calculate each element of the product matrix

$T=\begin{pmatrix}125(40)+160(25)+200(30)\\105(40)+95(25)+160(30)\end{pmatrix}$
$=\begin{pmatrix}5000+4000+6000\\4200+2375+4800\end{pmatrix}$
$=\begin{pmatrix}15000\\11375\end{pmatrix}.$

1. Interpret each element of $T$ using the row meanings of $W$ and the fee column matrix $C$

Since the rows of $W$ are beginners and advanced learners, and $C$ contains the fees for drama, writing and speech, the product
$T=\begin{pmatrix}15000\\11375\end{pmatrix}$
gives the total fees collected over 5 weekdays for each level.

So $15000$ is for beginners and $11375$ is for advanced learners.