1. The problem describes a system of components and blends connected by variables $x_{ij}$, where $i$ indexes components and $j$ indexes blends. 2. To analyze or solve such a system, we typically represent it as a matrix $X = \begin{bmatrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \\ x_{41} & x_{42} & x_{43} \end{bmatrix}$, where each entry corresponds to the flow or connection from component $i$ to blend $j$. 3. Without additional equations or constraints, the problem is to understand or manipulate this matrix representation. 4. If the goal is to find relationships or solve for variables, we need equations relating these $x_{ij}$ values, such as sum constraints or balance equations. 5. Since no explicit equations or numerical values are given, the solution is to express the system as the matrix $X$ shown above, representing all connections from components to blends. Final answer: $$X = \begin{bmatrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \\ x_{41} & x_{42} & x_{43} \end{bmatrix}$$ This matrix summarizes the connections from each component to each blend.