表格显示了按星期几和不同年龄组分类的电影票价格。

1. Write the ticket prices in matrix form using the given row and column categories.

Rows: Child, Adult, Senior Citizen.
Columns: Monday to Thursday, Friday, Saturday and Sunday.

$$P=\begin{pmatrix} 6.00&8.50&9.00\\ 7.00&10.00&12.50\\ 6.50&9.00&10.00 \end{pmatrix}$$

1. Form the $2\times3$ matrix using families as rows and age groups as columns.

Columns are in the order: Child, Adult, Senior Citizen.

Ng family: $1$ child, $2$ adults, $1$ senior citizen $\Rightarrow (1,2,1)$.

Tan family: $3$ children, $2$ adults, $0$ senior citizens $\Rightarrow (3,2,0)$.

$$Q=\begin{pmatrix} 1&2&1\\ 3&2&0 \end{pmatrix}$$

1. Multiply $Q$ and $P$ using row-by-column products.

Using

$$Q=\begin{pmatrix}1&2&1\\3&2&0\end{pmatrix},\quad P=\begin{pmatrix} 6.00&8.50&9.00\\ 7.00&10.00&12.50\\ 6.50&9.00&10.00 \end{pmatrix},$$ $$QP=\begin{pmatrix} 1(6.00)+2(7.00)+1(6.50)&1(8.50)+2(10.00)+1(9.00)&1(9.00)+2(12.50)+1(10.00)\\ 3(6.00)+2(7.00)+0(6.50)&3(8.50)+2(10.00)+0(9.00)&3(9.00)+2(12.50)+0(10.00) \end{pmatrix}$$ $$=\begin{pmatrix} 26.50&37.50&44.00\\ 32.00&45.50&52.00 \end{pmatrix}.$$

2. Explain the meaning of the elements of $QP$.

Since rows of $Q$ represent the families and columns of $P$ represent the day categories, the entries of $QP$ represent the total ticket costs for each family on each type of day.

Rows: Ng family, Tan family.

Columns: Monday to Thursday, Friday, Saturday and Sunday.