Question

consider the given network. organize the data in matrix form.

\\(x = \

$$\begin{bmatrix} 0 & 1 & 0 \\\\ 1 & 0 & 0 \\\\ 0 & 0 & 0 \\end{bmatrix}$$

\\)

Explanation:

Identify the vertices and connections

Using the Network Representation knowledge point

• Vertices: \(P, Q, R\)
• Edges: Undirected edge between \(P\) and \(Q\)
• Isolated vertex: \(R\) has no connections

Set up the adjacency matrix structure

Using the Adjacency Matrix Construction knowledge point

• Rows and columns ordered alphabetically: \(P, Q, R\)
• Row 1 / Column 1: \(P\)
• Row 2 / Column 2: \(Q\)
• Row 3 / Column 3: \(R\)

Determine matrix elements

Using the Adjacency Matrix Construction knowledge point

$$ X =
LATEXBLOCK0
$$

• \(x_{PQ} = x_{QP} = 1\) (connected)
• All other entries are \(0\) (no loops, no other connections)

$$ X =
LATEXBLOCK1
$$

Answer:

• **(A) \(X =

$$\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

\) (Correct answer)**