A tour agency records the total number of people buying tour packages to Thailand and Vietnam in the months of November and December. In November, 144 people bought the Thailand tour package and 100 people bought the Vietnam tour package. In December, 208 people bought the Thailand tour package and 180 people bought the Vietnam tour package. This information can be represented by the matrix $M=\begin{pmatrix}144 & 100\\208 & 180\end{pmatrix}$ where the first row represents November, the second row represents December, and the columns (from left to right) represent Thailand and Vietnam respectively.

1. Arrange the two package prices as a $2\times1$ column matrix in the stated order

Thailand price $=\char36{}890$, Vietnam price $=\char36{}750$.

Since the columns of $M$ are ordered as Thailand, then Vietnam,
$K=\begin{pmatrix}890\\750\end{pmatrix}.$

1. Substitute $M$ and $K$ into $R=MK$ and multiply row by column

From part (a),
$K=\begin{pmatrix}890\\750\end{pmatrix}.$
Hence
$R=MK=\begin{pmatrix}144&100\\208&180\end{pmatrix}\begin{pmatrix}890\\750\end{pmatrix}$
$=\begin{pmatrix}144(890)+100(750)\\208(890)+180(750)\end{pmatrix}$
$=\begin{pmatrix}128160+75000\\185120+135000\end{pmatrix}$
$=\begin{pmatrix}203160\\320120\end{pmatrix}.$

1. Identify the meaning of each element in $R$ from the matrix multiplication context

Since $R=MK$, each element is obtained by multiplying the number of people buying each package by its price and adding the amounts for Thailand and Vietnam.

Thus, the first element of $R$ is the total revenue for November, and the second element is the total revenue for December.

1. Substitute $R$ and multiply the row matrix by the column matrix

From part (b),
$R=\begin{pmatrix}203160\\320120\end{pmatrix}$

2. Multiply by $\frac12$ and state the contextual meaning

Since $203160$ and $320120$ are the total amounts collected in November and December respectively, $\frac12(1\;1)R$ is the average amount collected per month over the two months.