Question

the table below shows business activity for one month in a home-improvement store. the table shows stock, sales, and deliveries. write the given data in 2*3 matrix form.

\

$$\begin{tabular}{|c|c|c|c|} \\hline & stock & sales & deliveries \\\\ \\hline picnic table & 20 & 25 & 30 \\\\ \\hline bq grills & 20 & 10 & 12 \\\\ \\hline \\end{tabular}$$

\\( a = \

$$\begin{bmatrix} 25 & 30 & 20 \\\\ 10 & 12 & 20 \\end{bmatrix}$$

\\)

\\( a = \

$$\begin{bmatrix} 20 & 25 & 30 \\\\ 20 & 10 & 12 \\end{bmatrix}$$

\\)

Explanation:

Identify the dimensions and layout of the matrix

The problem asks for a \(2 \times 3\) matrix (2 rows and 3 columns) representing the given table data.
The rows correspond to the items:

• Row 1: Picnic table
• Row 2: BQ grills

The columns correspond to the categories:

• Column 1: Stock
• Column 2: Sales
• Column 3: Deliveries

Map the table values to the matrix elements

Using the table values:

• Row 1 (Picnic table): \(20\), \(25\), \(30\)
• Row 2 (BQ grills): \(20\), \(10\), \(12\)

This yields the matrix:

$$ A =
LATEXBLOCK0
$$

Match with the given options

Comparing the derived matrix with the choices:

• Option 1: \(A =

$$\begin{bmatrix} 25 & 30 & 20 \\ 10 & 12 & 20 \end{bmatrix}$$

\)

• Option 2: \(A =

$$\begin{bmatrix} 20 & 25 & 30 \\ 20 & 10 & 12 \end{bmatrix}$$

\)

The second option is the correct representation.

Answer:

• (A) \(A =

$$\begin{bmatrix} 25 & 30 & 20 \\ 10 & 12 & 20 \end{bmatrix}$$

\)

• **(B) \(A =

$$\begin{bmatrix} 20 & 25 & 30 \\ 20 & 10 & 12 \end{bmatrix}$$

\) (Correct answer)**