A family is planning to rent a house for summer vacation. The family is undecided on whether to travel to Orlando, Tampa, or Miami. The following table shows the number and type of houses available in each location.

\begin{tabular}{|c|c|c|c|}
\hline
City & 1-Bedroom & 2-Bedroom & 3-Bedroom \\
\hline
Orlando & 6 & 9 & 25 \\
\hline
Tampa & 24 & 12 & 18 \\
\hline
Miami & 17 & 13 & 21 \\
\hline
\end{tabular}

Which of the following matrices represents the number of each type of house available in Miami?

A. [tex]\(\begin{pmatrix} 6 & 9 & 25 \end{pmatrix}\)[/tex]
B. [tex]\(\begin{pmatrix} 24 & 12 & 18 \end{pmatrix}\)[/tex]
C. [tex]\(\begin{pmatrix} 17 & 13 & 21 \end{pmatrix}\)[/tex]
D. [tex]\(\begin{pmatrix} 25 & 18 & 21 \end{pmatrix}\)[/tex]



Answer :

To answer the question regarding the number of each type of house available in Miami, we will refer to the data given for Miami in the provided table:

[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{City} & \text{1-Bedroom} & \text{2-Bedroom} & \text{3-Bedroom} \\ \hline \text{Orlando} & 6 & 9 & 25 \\ \hline \text{Tampa} & 24 & 12 & 18 \\ \hline \text{Miami} & 17 & 13 & 21 \\ \hline \end{array} \][/tex]

For the city Miami:
- The number of 1-Bedroom houses is 17.
- The number of 2-Bedroom houses is 13.
- The number of 3-Bedroom houses is 21.

To represent this information in matrix form, we will create a row vector (1x3 matrix) where each element corresponds to the number of houses of each type available in Miami.

Thus, the matrix for Miami is:

[tex]\[ \begin{bmatrix} 17 & 13 & 21 \end{bmatrix} \][/tex]

Therefore, the correct matrix representing the number of each type of house available in Miami is [tex]\(\begin{bmatrix} 17 & 13 & 21 \end{bmatrix}\)[/tex].