Linear Algebra Word Problem
I am really stuck on this problem....
An economy consists of five sectors-agriculture,manufacturing, services, entertainment, and mining. For each unit of output, agriculture used .25 unit of its own output, .40 unit from manufacturing, .10 unit from services, .02 unit from entertainment, and .03 unit from mining. For each unit of output, manufacturing uses .40 unit of its own output, .15 unit from agriculture, .10 unit from services, .03 unit from entertainment, and .20 unit from mining. For each unit of output, services use .25 unit of its own output, .10 unit from agriculture. .15 from manufacturing, .06 unit from entertainment, and .02 from mining. For each unit of output, entertainment uses .15 unit of its own output, .06 unit from agriculture, .45 unit from manufacturing, .10 unit from services, and .05 unit from mining. For each unit of output, mining uses .08 of its own output, .05 unit from agriculture, .55 unit from manufacturing, .20 unit from services, and .05 unit from entertainment.
1. construct a table that illustrates the inputs consumed per unit of output.
2. A) determine what the individual intermediate demands are created if agriculture plans to produce 240 units, manufacturing 160 units, services 125 units, entertainment 90 units, and mining 120 units.
B) construct the consumption matrix C for this economy and use the matrix to compute the total intermediate demand from all 5 sectors if the amounts produced for each sector are as given from part A).
3. Develop a system of equations that can be used to determine the production levels needed to satisfy a final demand of 60 units for agriculture, 20 units for manufacturing, 10 units for services, 30 units for entertainment, and 10 units for mining. Round-off answer to 2 decimal places (calculator).
4. Use your calculator to obtain an inverse matrix and use the inverse to determine the production levels needed to satisfy a final demand as specified in question 3. Round-off your answer to two decimal places. How do the answers in question 3 and question 4 compare?
5. Give the inverse matrix that you used in question 4. Round-off its entires to four decimal places. What matrix operation did you use in question 4 to compute production levels? Specify.
question to linear algebra word problem
hi im still confussed on parts 4 and 5. i received my answer for part three and when i solve part for they dont match up so i think i have the wrong matrix???