Problem 6.3. A Linear Economic model This question is a simple application of matrices and linear system of equations to an economic system commonly known as \"Leontief Closed Model\". In 1973 Wassily Leontief was awarded the Norbel prize in economics for his work on mathematical models. Roughly speaking, an economic system consists of several industries, each of which produces a product and each of which uses some of the production of the other industries. The following question is a typical example. Consider a society consisting of three members: a farmer, carpenter, and a tailor. Each produces one commodity: the farmer grows the food, the carpenter builds homes, and the tailor makes clothes. For convenience, we may select our units so that each individual produces one unit of each commodity during the year. Suppose that during the year, the portion of each commodity that is consumed by each individual is given in the following Table. As an example, the Carpenter consumes 0.3 unit of the Farmer's product, 0.3 unit of his own product and 0.4 of the Tailor's product. The same interpretation applies for the Farmer and Tailor. Find the annual prices that each member must charge for its income to equal its expenditures