一家旅行社记录了在十一月和十二月购买泰国和越南旅游套餐的总人数。 十一月，有 144 人购买了泰国旅游套餐，100 人购买了越南旅游套餐。 十二月，有 208 人购买了泰国旅游套餐，180 人购买了越南旅游套餐。 这些信息可以用矩阵 $M=\begin{pmatrix}144 & 100\\208 & 180\end{pmatrix}$ 表示，其中第一行代表十一月，第二行代表十二月，各列（从左到右）分别代表泰国和越南。

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.