Question

question 17 points 2

a school recorded the number of students enrolled in three different clubs:

• 12 students in the art club
• 18 students in the drama club
• 14 students in the music club

how can this data be represented in matrix form?

\\(\bigcirc\\ 12\quad 18\quad 14\\)

\\(\bigcirc\\ \

$$\begin{bmatrix} 12 \\\\ 18 \\\\ 14 \\end{bmatrix}$$

\\)

Explanation:

Identify the given data

Using the Matrix Representation knowledge point
The problem lists enrollment numbers for three distinct categories:

• Art club: 12 students
• Drama club: 18 students
• Music club: 14 students

Determine the matrix dimensions

Using the Matrix Dimensions knowledge point
A single list of three numerical values can be organized as a row vector of dimension \(1 \times 3\) or a column vector of dimension \(3 \times 1\).

Match with the given options

Using the Matrix Representation knowledge point

• Option 1: \(

$$\begin{bmatrix} 12 & 18 & 14 \end{bmatrix}$$

\) is a \(1 \times 3\) row matrix.

• Option 2: \(

$$\begin{bmatrix} 12 \\ 18 \\ 14 \end{bmatrix}$$

\) is a \(3 \times 1\) column matrix.
Both are mathematically valid representations of a single data list. However, looking closely at the image, the first option has a double bracket on the right side \([12 \quad 18 \quad 14]\|\), which is a typographical error or formatting artifact. The second option is a standard, properly formatted column matrix \(

$$\begin{bmatrix} 12 \\ 18 \\ 14 \end{bmatrix}$$

\).

Answer:

• (A) \(

$$\begin{bmatrix} 12 & 18 & 14 \end{bmatrix}$$

\)

• **(B) \(

$$\begin{bmatrix} 12 \\ 18 \\ 14 \end{bmatrix}$$

\) (Correct answer)**