An economy consists of three interdependent sectors; agriculture, mining and manufacturing. The flow of inputs and outputs between the sectors is represented in the table below: Inputs (Tons) Final demand Total Output Output (Tons) Agriculture Mining Manufacturing Agriculture 20,000 32,500 37,500 10,000 100,000 Mining 30,000 65,000 37,500 30,000 162,500 Manufacturing 40,000 32,500 12,500 40,000 125,000 Required: a) The technical coefficient matrix (4 marks) b) The Leontief inverse matrix (7 marks) c) The output level for each sector of the final demand for the agricultural sector increases by 1000 tons and that of the manufacturing sector falls by 500 tons and the final demand for the mining sector remains unchanged. (4 marks