Suppose an economy consists of three sectors: Mining, Energy and Transportation. The output of each sector is distributed among the various sectors, as shown in the table below. A sector looks down a column to see where its output goes, and it looks across a row to see what it needs as inputs. For instance, the second column says that Energy sells 40% of its output to Mining and 50% to Transportation, and retains the rest. The first row says that Mining receives (pays for) 40% of the Energy output and 60% of Transportation output. Distribution of Output from: Mining Energy Transportation Purchased by: 0.0 0.4 0.6 Mining 0.6 0.1 0.2 Energy 0.4 0.5 0.2 Transportation Equilibrium prices can be assigned to the total outputs of the sectors such that each sector's income exactly balances its expense. We want to find the equilibrium prices for the annual outputs of these three sectors: Mining, Energy, and Transportation. (a) Let x, y, z be the equilibrium prices of the annual outputs of Mining, Energy, and Transportation, respectively. Show that we can construct the following system of linear equations from the given information