Suppose an economic system with three industries whose external demands are 10, 25, and 20 respectively.

Also, the coefficients of the technological matrix are:

a₁₁ = 0.2

a₁₂ = 0.5

a₁₃ = 0.15

a₂₁ = 0.4

a₂₂ = 0.1

a₂₃ = 0.3

a₃₁ = 0.25

a₃₂ = 0.5

a₃₃ = 0.15

Build the technological matrix, the Leontief matrix and state the system of equations in its matrix form. Solve the system to determine the output needed by the three industries to satisfy the total demand in the economy, that is, find the output needed so that supply is approximately equal to demand.