Question 1:

1 .63 Question HelpV 0 Consider an economy With three sectors, Chemicals & Metals, Fuels & Power, and Machinery Chemicals sells 30% at its output to Fuels and 50% to Machinery and retains the rest. Fuels sells 80% of its output to Chemicals and 10% to Machinery and retains the rest Machinery sells 40% of its output to Chemicals and 50% to Fuels and retains the rest Complete parts (a) through (c) below. a. Construct the exchange table for this economy Distribution of Output from: Chemicals Fuels Machinery Purchased by: 0.20 0.80 0.40 Chemicals 0 30 0.10 0.50 Fuels 050 0.10 0.10 Machinery (Type Integers or decimals.) b. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced to nd these prices. The rst, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respedively The augmented matrix is . (Type an integer or decimal tor each matrix element) Suppose the solution set of a certain system of inear equations can be described as x1 : 5 + 4x3. x2 : 5 6x3, with x3 free. Use vectors to describe this set as a line in R3. Geometrically. the solution set is a line through parallel to Find the value(s} of h for which the vectors are linearly dependent. Justify your answer. 1 -3 4 -2 , 7 , 1 4 6 h The value{s) of h which makes the vectors linearly dependent is(are) (Use a comma to separate answers as needed} :I because this will cause : to bea : variable