Question

there are three classes, a, b, and c in a school. class a has 24 boys and 13 girls. class b has 15 boys and 40 girls. class c has 12 boys and 16 girls. represent the given data in a 2*3 matrix. if the matrix is x, find \\(x_{22}\\).

\\(x = \

$$\begin{bmatrix} 24 & 15 & 12 \\\\ 13 & 40 & 16 \\end{bmatrix}$$

, x_{22} = 40\\)

\\(x = \

$$\begin{bmatrix} 24 & 40 & 12 \\\\ 13 & 15 & 16 \\end{bmatrix}$$

, x_{22} = 15\\)

Explanation:

Identify matrix dimensions and layout

Using the Matrix Dimensions knowledge point

$$ \text{Rows} = 2, \quad \text{Columns} = 3 $$

The rows represent gender (boys in row 1, girls in row 2), and columns represent classes (A, B, and C).

Construct the matrix representation

Using the Matrix Representation knowledge point

$$ X =
LATEXBLOCK0
$$

Find the specified element

Using the Matrix Element Indexing knowledge point

$$ X_{22} = 40 $$

Answer:

• **(A) \(X =

$$\begin{bmatrix} 24 & 15 & 12 \\ 13 & 40 & 16 \end{bmatrix}$$

, X_{22} = 40\) (Correct answer)**

• (B) \(X =

$$\begin{bmatrix} 24 & 40 & 12 \\ 13 & 15 & 16 \end{bmatrix}$$

, X_{22} = 15\)