Finite Math Problem?

Question

For the input-output matrix A, find the output required to meet the demand D.

A= {0.2, 0.4} D= (700)
....{0.3, 0.6} ......... (400)

Possible answers are the following:
a. (2, -1)
(4, 1)

b. (-6, 3)
(-6, 3)

c. (6, -3)
(9, 0)

d. (10, -5)
(14, -1)

Answer 1

The answers don't seem to make sense. The output is normally a column vector, not a matrix; multiplying the matrix by the output vector gives a vector corresponding to inter-industry demand, and subtracting this from the output gives the final (external) demand satisfied.

If the output is X, then we have
X = AX + D
<=> (I-A) X = D
So we get the augmented matrix
[0.8 -0.4 | 700]
[-0.3 0.4 | 400]
~
[1 -0.5 | 875]
[0 0.25 | 662.5]
~
[1 0 | 2200]
[0 1 | 2650]

and so the gross output required is (2200, 2650).

It doesn't make sense to me that from two matrices with elements on the order of 1 you can get a result on the order of 100. If they're well-behaved, anyway. ;-)

I thought you might be looking for the inverse of I-A, but this turns out to be {(2, 2); (1.5, 4)} (i.e. [2 2] is the first row and [1.5 4] is the second row), which isn't one of your answers.