Question: The figure shows a food web with animals $E$, $F$, $G$, and $H$. The arrows indicate the food sources of each population. For example, animal $G$ feeds on animal $H$. (a) Write a matrix $C$ in which each row and column represent a population in the food chain. Enter a $1$ when the population in a given row feeds on the population in the given column. Otherwise, enter a $0$.
1. **State the problem:** We need to create a matrix $C$ representing the feeding relationships among populations $E$, $F$, $G$, and $H$. Each row and column corresponds to one animal. A $1$ indicates the row animal feeds on the column animal; $0$ otherwise.
2. **Identify feeding relationships from the description:**
- $E$ feeds on $F$, $G$, and $H$.
- $F$ feeds on $G$.
- $G$ feeds on $H$.
- $H$ feeds on none.
3. **Construct the matrix $C$:** Rows and columns are ordered as $E$, $F$, $G$, $H$.
$$
C = \begin{bmatrix}
0 & 1 & 1 & 1 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0
\end{bmatrix}
$$
4. **Explanation:**
- Row $E$: $E$ feeds on $F$, $G$, $H$ so entries in columns $F$, $G$, $H$ are $1$.
- Row $F$: $F$ feeds on $G$ only.
- Row $G$: $G$ feeds on $H$ only.
- Row $H$: $H$ feeds on none, so all zeros.
This matrix fully represents the food web feeding relationships.