Question

the weights of three boys and three girls in kg are 45, 42, 56 and 53, 51, and 40, respectively. use 23 and 32 matrices to represent the data.

\\(a = \

$$\begin{bmatrix} 45 & 42 & 56 \\\\ 53 & 51 & 40 \\end{bmatrix}$$

, b = \

$$\begin{bmatrix} 45 & 53 \\\\ 42 & 51 \\\\ 51 & 56 \\end{bmatrix}$$

\\)

\\(a = \

$$\begin{bmatrix} 45 & 42 & 56 \\\\ 53 & 51 & 40 \\end{bmatrix}$$

, b = \

$$\begin{bmatrix} 45 & 53 \\\\ 42 & 51 \\\\ 56 & 40 \\end{bmatrix}$$

\\)

Explanation:

Identify the given data

The weights of three boys are \(45\text{ kg}\), \(42\text{ kg}\), and \(56\text{ kg}\).
The weights of three girls are \(53\text{ kg}\), \(51\text{ kg}\), and \(40\text{ kg}\).

Define the matrix dimensions

We need to represent this data using:

• A \(2 \times 3\) matrix (2 rows, 3 columns), let's call it \(A\).
• A \(3 \times 2\) matrix (3 rows, 2 columns), let's call it \(B\).

Construct the \(2 \times 3\) matrix

For matrix \(A\) of size \(2 \times 3\):

• Row 1 represents the boys' weights: \([45, 42, 56]\).
• Row 2 represents the girls' weights: \([53, 51, 40]\).

$$ A =
LATEXBLOCK0
$$

Construct the \(3 \times 2\) matrix

For matrix \(B\) of size \(3 \times 2\):

• Column 1 represents the boys' weights: \([45, 42, 56]^T\).
• Column 2 represents the girls' weights: \([53, 51, 40]^T\).
• Each row represents a pair of a boy and a girl (e.g., Row 1 has the first boy and first girl).

$$ B =
LATEXBLOCK1
$$

Compare with the options

• The first option shows:

$$ A =
LATEXBLOCK2
, \quad B =
LATEXBLOCK3
$$

This is incorrect because the last row of \(B\) has incorrect values.

• The second option shows:

$$ A =
LATEXBLOCK4
, \quad B =
LATEXBLOCK5
$$

This matches our constructed matrices perfectly.

Answer:

• (A) \(A =

$$\begin{bmatrix} 45 & 42 & 56 \\ 53 & 51 & 40 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 45 & 53 \\ 42 & 51 \\ 51 & 56 \end{bmatrix}$$

\)

• **(B) \(A =

$$\begin{bmatrix} 45 & 42 & 56 \\ 53 & 51 & 40 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 45 & 53 \\ 42 & 51 \\ 56 & 40 \end{bmatrix}$$

\) (Correct answer)**