Question

the type of televisions used in households is given. create a matrix based on the given data.

\

$$\begin{tabular}{|c|c|c|c|} \\hline type & 1975 & 1980 & 1985 \\\\ \\hline black \\& white & 55 & 45 & 35 \\\\ \\hline color & 65 & 75 & 85 \\\\ \\hline \\end{tabular}$$

\\( x = \

$$\begin{bmatrix} 55 & 45 & 35 \\\\ 65 & 75 & 85 \\end{bmatrix}$$

\\)

\\( x = \

$$\begin{bmatrix} 55 & 65 & 35 \\\\ 45 & 75 & 85 \\end{bmatrix}$$

\\)

Explanation:

Identify the data structure

Using the Matrix Representation and Matrix Construction knowledge points

$$ \text{Table Rows: }
LATEXBLOCK0
$$

$$ \text{Table Columns: }
LATEXBLOCK1
$$

Map table values to matrix elements

Using the Matrix Construction knowledge point

$$
LATEXBLOCK2
$$

Construct the final matrix

Using the Matrix Representation knowledge point

$$ X =
LATEXBLOCK3
$$

Answer:

• **(A) \(X =

$$\begin{bmatrix} 55 & 45 & 35 \\ 65 & 75 & 85 \end{bmatrix}$$

\) (Correct answer)**

• (B) \(X =

$$\begin{bmatrix} 55 & 65 & 35 \\ 45 & 75 & 85 \end{bmatrix}$$

\)