Consider a system with the following state-space representation X(t) = [₁]x(t) + B₂Ju What values of b, and b₂ are required so that the system is controllable?

23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.