1. **State the problem:** Rewrite the system of differential equations in matrix notation with clear rows and columns. 2. **Matrix notation:** The system can be written as $$\frac{d}{dt}\begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_n \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{bmatrix} \begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_n \end{bmatrix}$$ 3. **Explanation:** Here, $\vec{y} = \begin{bmatrix} y_1 & y_2 & \cdots & y_n \end{bmatrix}^T$ is the vector of unknown functions, and $A = \begin{bmatrix} a_{ij} \end{bmatrix}$ is the coefficient matrix. 4. **Purpose:** Writing the system this way clarifies the structure and makes it easier to apply linear algebra techniques like eigenvalue decomposition. 5. **Summary:** The question requires expressing the system as $$\vec{y}' = A \vec{y}$$ with $A$ explicitly shown as a matrix with rows and columns representing coefficients of each equation.