A simple economy consists of three industries: agriculture, manifacturing and services.
The 3x3 input-output matrix associated with this economy is
A M S
A 0.1 0.1 0.2
M 0.1 0.2 0.1
S 0.1 0.2 0.2

Find the gross output of goods needed to satisfy a consumer demand for 110 million dollars worth of agricultural products, 140 million dollars worth of manufactured products, and 180 million dollars worth of services.

Question

A simple economy consists of three industries: agriculture, manifacturing and services. 
The 3x3 input-output matrix associated with this economy is
          A 	  M 	  S 
  A 	 0.1 	 0.1 	 0.2 
  M 	 0.1 	 0.2 	 0.1 
  S 	 0.1 	 0.2 	 0.2

Find the gross output of goods needed to satisfy a consumer demand for 110 million dollars worth of agricultural products, 140 million dollars worth of manufactured products, and 180 million dollars worth of services.

anonymous · Answer

i'm not supposed to get a negative value for agriculture right?

anonymous · Answer

No, I got a negative value too but it's wrong.

dumbcow · Answer

I also get a -400 for agriculture, are you sure the matrix is correct, maybe one of the numbers is negative

anonymous · Answer

@dumbcow, mind explaining how you get your -400? because i'm also a newbie in matrix. just learnt it about 2weeks ago, is it appropriate to use row-reduced method?

dumbcow · Answer

im assuming so.
using matrix algebra
$$AX = B$$
$$\rightarrow X = A^{-1}*B$$

i set B = [110, 140, 180]

dumbcow · Answer

row reduced form yields the same results as above ^^

anonymous · Answer

Yeah I'm sure the numbers are correct. Do you know any other way to solve it? Please help if you can because the assignment is due in an hour.