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 matrix dimensions and structure

The problem asks to write the given table data in a \(2 \times 3\) matrix form.
A \(2 \times 3\) matrix has 2 rows and 3 columns.

Map table rows and columns to matrix elements

The table has 2 rows of data (excluding headers):

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

The table has 3 columns of data (excluding row labels):

• Column 1 (Stock): 20, 20
• Column 2 (Sales): 25, 10
• Column 3 (Deliveries): 30, 12

Construct the matrix

Placing the elements in their corresponding row and column positions:

$$ A =
LATEXBLOCK0
$$

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)**