i have an input output matrix problem I don't know how to complete for homework.

Question

My homework is asking "Suppose the following matrix represents the input-output matrix of a simplified economy that involves just three commodity categories: Manufacturing, Agriculture, and Transportation. How many units of each commodity should be produced to satisfy a demand of 1100 Units for each commodity?" the matrix is

MFG AGRI TRANS

MFG 0 1/4 1/3

AGRI 1/2 0 1/4

TRA 1/4 1/4 0

Answer 1

So let's call your input/output matrix B

Then the question is actually asking to find [M, T, A] such that

B [M A T] = [1100,1100,1100].

Acutally, both [M A T] and [1100 1100 1100} should be vertical vectors, but whatever, let's proceed.

In order to solve this equation, you must multiply both sides by B^-1 , to get

[M A T] = B^-1 [1100 1100 1100]

to get

M = 1600

A = 2800

T = 1200