Chapter 4, Problem 14MCQ

(a)

To determine

To find: The matrix A to represent the regular season stock.

Answer to Problem 14MCQ

The required matrix is $\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Size	Small	Medium	Large
Child	10	10	15
Adult	25	35	45

Table 1

Calculation:

From the table, the matrix A to represent the regular season stock is,

  $\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]$

(b)

To determine

To find: The scalar that can be used to determine a matrix M to represent the new numbers.

Answer to Problem 14MCQ

The required matrix is $\left[\begin{array}{ccc}20& 20& 30\\ 50& 70& 90\end{array}\right]$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Size	Small	Medium	Large
Child	10	10	15
Adult	25	35	45

Table 1

Calculation:

Consider the matrix A is used to represent the regular season stock and the matrix M is the double the stock represented in matrix A as,

  $M=2A$

Then,

  $\begin{array}{c}M=2\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]\\ =\left[\begin{array}{ccc}20& 20& 30\\ 50& 70& 90\end{array}\right]\end{array}$

(c)

To determine

To find: The value of $M-A$ and what does it resembles.

Answer to Problem 14MCQ

The value of matrix $M-A$ is $\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]$ and it represents the number of shirts used for the playoff games.

Explanation of Solution

Given:

The given table is shown in Table 1

Size	Small	Medium	Large
Child	10	10	15
Adult	25	35	45

Table 1

Calculation:

The matrix $M-A$ represents the number of shirts used for the playoff games.

  $\begin{array}{c}M-A=\left[\begin{array}{ccc}20& 20& 30\\ 50& 70& 90\end{array}\right]-\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]\\ =\left[\begin{array}{ccc}10& 10& 15\\ 25& 35& 45\end{array}\right]\end{array}$