An important application in the study of economics is the study of the relationship between industrial production and consumer demand. In creating an economic model, Russian-American economist Wassily Leontief (1906-1999) noted that the total output less the internal consumption equals consumer demand. Mathematically his input-output model looks like [X] - [A][X] = [D], where [X] is the total output matrix, [A] is the input-output matrix, and [D] is the matrix representing consumer demand.
Here is an input-output matrix, [A], for a simple three-sector economy:

For instance, the first column tells the economist that to produce an output of 1 unit of agricultural products requires the consumption (input) of 0.2 unit of agricultural products, 0.2 unit of manufacturing products, and 0.1 unit of service products.
The demand matrix, [D], represents millions of dollars. Use the equation [X] - [A][X] = [D] to find the output matrix, [X].

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Output Agriculture 02 02 Manufocturing 02 04 A Servic 0.1 0.2 03 100 [D]=| 80