Question

there are two boys and a girl, anthony, kevin, and lisa. anthony gives money to lisa. kevin gives money to anthony and lisa. lisa gives money to anthony. organize the given data in matrix form.

\\(a = \

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

\\)

\\(a = \

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

\\)

Explanation:

Define the network vertices and order

Using the Matrix Representation knowledge point

$$ \text{Vertices: } \{v_1: \text{Anthony}, v_2: \text{Kevin}, v_3: \text{Lisa}\} $$

Construct the adjacency matrix elements

Using the Adjacency Matrix Construction and Directed Graph knowledge points

$$
LATEXBLOCK0
$$

Formulate the final matrix

Using the Matrix Representation knowledge point

$$ A =
LATEXBLOCK1
$$

Answer:

• **(A) \(A =

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

\) (Correct answer)**

• (B) \(A =

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

\)