Question

an electronics company records each type of entertainment devices sold at three of their stores so that they can monitor the purchase of goods. the sales in a month are shown below. use a matrix to represent the given data.

\

$$\begin{tabular}{|c|c|c|c|} \\hline & speaker & computer & mobile \\\\ \\hline shop 1 & 45 & 65 & 110 \\\\ \\hline shop 2 & 60 & 70 & 122 \\\\ \\hline shop 3 & 95 & 55 & 132 \\\\ \\hline \\end{tabular}$$

\\( x = \

$$\begin{bmatrix} 45 & 65 & 110 \\\\ 60 & 70 & 122 \\\\ 95 & 55 & 132 \\end{bmatrix}$$

\\)

\\( x = \

$$\begin{bmatrix} 45 & 65 & 110 \\\\ 60 & 45 & 122 \\\\ 95 & 55 & 132 \\end{bmatrix}$$

\\)

Explanation:

Identify the data table structure

Using the Matrix Representation knowledge point
The given table has rows representing shops and columns representing devices:

• Row 1 (Shop 1): 45, 65, 110
• Row 2 (Shop 2): 60, 70, 122
• Row 3 (Shop 3): 95, 55, 132

Construct the corresponding matrix

Using the Matrix Construction knowledge point

$$ X =
LATEXBLOCK0
$$

Match with the given options

We compare our constructed matrix with the choices:

• Option 1:

$$ X =
LATEXBLOCK1
$$

• Option 2:

$$ X =
LATEXBLOCK2
$$

The first option matches the table data exactly.

Answer:

• **(A) \(X =

$$\begin{bmatrix} 45 & 65 & 110 \\ 60 & 70 & 122 \\ 95 & 55 & 132 \end{bmatrix}$$

\) (Correct answer)**

• (B) \(X =

$$\begin{bmatrix} 45 & 65 & 110 \\ 60 & 45 & 122 \\ 95 & 55 & 132 \end{bmatrix}$$

\)