Chapter 4, Problem 11SGR

a.

To determine

To describe: The matrix to represent the number of customers.

Answer to Problem 11SGR

The matrix to represent the number of customersis

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information thata table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

b.

To determine

To calculate: The dimension of the matrix that represent the number of customers.

Answer to Problem 11SGR

The dimension of the matrix is $2\times 3$ .

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information thata table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

Since, there are two rows and three columns so the dimension of the matrix is $2\times 3$ .

c.

To determine

To calculate: The value of $a_{23}$ from the matrix that represent the number of customers.

Answer to Problem 11SGR

The value of $a_{23}$ is $68$ .

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information that a table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

The entry $a_{23}$ corresponds to second row and third column entry of the matrix which is 68.

Thus, the value of $a_{23}$ is $68$ .

d.

To determine

To calculate: The value of $a_{11}$ from the matrix that represent the number of customers.

Answer to Problem 11SGR

The value of $a_{11}$ is $64$ .

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information that a table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

The entry $a_{11}$ corresponds to first row and first column entry of the matrix which is 64.

Thus, the value of $a_{11}$ is $64$ .

e.

To determine

To describe: The addition of elements of columns 1 and 2 in the matrix that represent the number of customers.

Answer to Problem 11SGR

The addition of elements of columns 1 and 2 is 223. This depicts the number of customers of both the types in store A and store B.

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information that a table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

The addition of elements of columns 1 and 2 is

  $64+42+108+9=223$

This depicts the number of customers of both the types that is adult and student in store A and store B.

f.

To determine

To describe: The interpretation if any if rows in the matrix that represent the number of customers are added.

Answer to Problem 11SGR

The addition of rows represent the number of customer in each store. Total number of customers in store A, store B and store C are106, 117 and 99 respectively.

Explanation of Solution

Given information:

A table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Calculation:

Consider the provided information that a table that depicts the type of customer in three different stores.

  $\begin{array}{cccc}\text{Type of Customer}& \text{Store A}& \text{Store B}& \text{Store C}\\ \text{adult }\left(\text{18 and older}\right)& 64& 108& 31\\ \text{student }\left(\text{ under 18}\right)& 42& 9& 68\end{array}$

Denote the three columns of the matrix as three different stores and 2 rows as type of customer in the store.

Therefore, the matrix to represent the number of customers is provided below,

  $\left[\begin{array}{ccc}64& 108& 31\\ 42& 9& 68\end{array}\right]$

The addition of rows is

  $\left[\begin{array}{ccc}106& 117& 99\end{array}\right]$

The addition of rows represent the number of customer in each store. Total number of customers in store A, store B and store C are 106, 117 and 99 respectively.