# Thread: Linear Equations and Matrices

1. ## Linear Equations and Matrices

A simple economy is based on 3 commodities: grain, fuel and transportation.
Production of 1 unit of grain requires 1/4 unit of fuel and 1/3 unit of transportation
Production of 1 unit of fuel requires 1/2 unit of grain and 1/4 unit of transportation,
Production of 1 unit of transportation requires 1/4 unit of grain and 1/4 unit of fuel.
Find the input-output matrix for this situation and the gross output required for a net production of 516 units of grain, 258 units of fuel and 129 units of transportation.

2. Originally Posted by vuze88
A simple economy is based on 3 commodities: grain, fuel and transportation.
Production of 1 unit of grain requires 1/4 unit of fuel and 1/3 unit of transportation
Production of 1 unit of fuel requires 1/2 unit of grain and 1/4 unit of transportation,
Production of 1 unit of transportation requires 1/4 unit of grain and 1/4 unit of fuel.
Find the input-output matrix for this situation and the gross output required for a net production of 516 units of grain, 258 units of fuel and 129 units of transportation.
G F T
G 1 1/4 1/3 | x | |561|
F 1/2 1 1/4 | y | = |258|
T 1/4 1/4 1 | z | |129|
It is in the form of A*X = P
SO X = A^-1*P