Chapter 6.6, Problem 5CYU

(a)

To determine

To write: the matrix to recognize the costs of an overnight stay at the hotel

Answer to Problem 5CYU

The matrix to recognize the costs of an overnight stay at the hotel is $\left[\begin{array}{cc}69& 89\\ 79& 109\\ 99& 139\end{array}\right]$ .

Explanation of Solution

Given:

A table showing costs of an overnight stay at a hotel is given.

Room	Weekday	Weekend
Single	$69	$89
Double	$79	$109
Suite	$99	$139

Calculation:

a. Following is the matrix which shows the costs of an overnight stay at hotel. In the following matrix first row shows the cost of Single room, second row shows the cost of Double room, third row shows the cost of Suite while first column shows the prices on weekdays and second column shows the prices on weekends.

  $\left[\begin{array}{cc}69& 89\\ 79& 109\\ 99& 139\end{array}\right]$

Conclusion:

Therefore, the matrix to recognize the costs of an overnight stay at the hotel is $\left[\begin{array}{cc}69& 89\\ 79& 109\\ 99& 139\end{array}\right]$ .

(b)

To determine

the dimensions of the matrix.

Answer to Problem 5CYU

Matrix has 3 rows and 2 columns. Therefore, it is a $\text{3}\times \text{2}$ matrix.

Explanation of Solution

Calculation:

  $\begin{array}{l}\left[\begin{array}{cc}69& 89\\ 79& 109\\ 99& 139\end{array}\right]3\text{ rows}\\ \text{2 columns}\end{array}$

Matrix has 3 rows and 2 columns. Therefore, it is a $\text{3}\times \text{2}$ matrix.

Conclusion:

Therefore, Matrix has 3 rows and 2 columns. Therefore, it is a $\text{3}\times \text{2}$ matrix.

(c)

To determine

To explain: which room and night is the most expensive.

Answer to Problem 5CYU

Suite room at weekend night is the most expensive and Single room at weekday night is the least expensive.

Explanation of Solution

Calculation:

  $\left[\begin{array}{cc}69& 89\\ 79& 109\\ 99& 139\end{array}\right]$

It is clear that the circled value is the smallest and squared value is the greatest, thus Suite room at weekend night is the most expensive and Single room at weekday night is the least expensive.

Conclusion:

Therefore, Suite room at weekend night is the most expensive and Single room at weekday night is the least expensive.