Question

there are 10 primary schools, 14 high schools, and 18 colleges in a town. represent the data in matrix form.

\\(a = \

$$\begin{bmatrix} 10 & 14 & 18 \\end{bmatrix}$$

\\), \\(b = \

$$\begin{bmatrix} 10 \\\\ 14 \\\\ 18 \\end{bmatrix}$$

\\)

\\(a = \

$$\begin{bmatrix} 10 & 14 & 18 \\end{bmatrix}$$

\\), \\(b = \

$$\begin{bmatrix} 14 \\\\ 10 \\\\ 18 \\end{bmatrix}$$

\\)

Explanation:

Identify the given data

Using the Matrix Representation knowledge point
The problem provides three data values representing the number of schools in a town:

• Primary schools: 10
• High schools: 14
• Colleges: 18

Construct row and column matrices

Using the Matrix Construction knowledge point

• A row matrix \(A\) organizes the data horizontally in a single row:

$$ A =
LATEXBLOCK0
$$

• A column matrix \(B\) organizes the same data vertically in a single column, maintaining the same order:

$$ B =
LATEXBLOCK1
$$

Compare with the given options

Using the Matrix Representation knowledge point

• The first option shows:

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

This correctly represents the data in both row and column formats.

• The second option shows:

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

This is incorrect because the order of elements in matrix \(B\) does not match the original data order.

Answer:

• **(A) \(A =

$$\begin{bmatrix} 10 & 14 & 18 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 10 \\ 14 \\ 18 \end{bmatrix}$$

\) (Correct answer)**

• (B) \(A =

$$\begin{bmatrix} 10 & 14 & 18 \end{bmatrix}$$

, B =

$$\begin{bmatrix} 14 \\ 10 \\ 18 \end{bmatrix}$$

\)