Question

timing | adult | children
before 10 a.m. | $20 | $10
10 a.m to 4 p.m | $50 | $25
after 4 p.m. | $75 | $30

write a matrix to represent the given data in both \\(3 \times 2\\) and \\(2 \times 3\\) matrix form.

\\(a = \

$$\begin{bmatrix} 20 & 50 \\\\ 10 & 25 \\\\ 75 & 30 \\end{bmatrix}$$

, b = \

$$\begin{bmatrix} 20 & 10 & 75 \\\\ 50 & 25 & 30 \\end{bmatrix}$$

\\)

\\(a = \

$$\begin{bmatrix} 20 & 10 \\\\ 50 & 25 \\\\ 75 & 30 \\end{bmatrix}$$

, b = \

$$\begin{bmatrix} 20 & 50 & 75 \\\\ 10 & 25 & 30 \\end{bmatrix}$$

\\)

Explanation:

Identify the data table values

Using the Matrix Representation knowledge point
The given table organizes pricing data by timing (rows) and age group (columns: Adult, Children):

• Before 10 A.M.: Adult = \$20, Children = \$10
• 10 A.M. to 4 P.M.: Adult = \$50, Children = \$25
• After 4 P.M.: Adult = \$75, Children = \$30

Construct the 3 x 2 matrix

Using the Matrix Dimensions knowledge point

$$ A =
LATEXBLOCK0
$$

Construct the 2 x 3 matrix

Using the Matrix Dimensions knowledge point

$$ B =
LATEXBLOCK1
$$

Match with the given options

Comparing our constructed matrices \(A\) and \(B\) to the choices:

• Option 1: \(A =

$$\begin{bmatrix} 20 & 50 \\ 10 & 25 \\ 75 & 30 \end{bmatrix}$$

\), \(B =

$$\begin{bmatrix} 20 & 10 & 75 \\ 50 & 25 & 30 \end{bmatrix}$$

\) (Incorrect)

• Option 2: \(A =

$$\begin{bmatrix} 20 & 10 \\ 50 & 25 \\ 75 & 30 \end{bmatrix}$$

\), \(B =

$$\begin{bmatrix} 20 & 50 & 75 \\ 10 & 25 & 30 \end{bmatrix}$$

\) (Correct)

Answer:

• (A) \(A =

$$\begin{bmatrix} 20 & 50 \\ 10 & 25 \\ 75 & 30 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 20 & 10 & 75 \\ 50 & 25 & 30 \end{bmatrix}$$

\)

• **(B) \(A =

$$\begin{bmatrix} 20 & 10 \\ 50 & 25 \\ 75 & 30 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 20 & 50 & 75 \\ 10 & 25 & 30 \end{bmatrix}$$

\) (Correct answer)**