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Question:

Consider the production model x = Cx + d for an economy with two sectors, where
C=
0.0 0.5
0.6 0.2

and

d=
50
30

Use an inverse matrix to determine the production level necessary to satisfy the final demand.

Answer:
110
120

C and d are both matrix, I wasn't sure how to format it on here.

I'm currently studying for a test and this question and answer were both in the book, I can't seem to figure out how they got the answer.

I saw an example of a similar problem here: http://alistairsavage.ca/mat1302/exercises/mat1302-input-output-model-exercises-solutions.pdf --but this method

For some reason, that method wasn't bringing me to the correct answer.. If you could please provide step-by-step instruction on how to do this it'd be a huge help, thanks!

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Equation: X = (I - A)^-1 x D

[1 0] [0 .5] [1 -.5] [1.6 1] minus = multiply by ^-1 (inverse) = [0 1] [.6 .2] [-.6 .8] [1.2 2]

[1.6 1] [50] [110] x(by D) = [1.2 2] [30] [120]

Answer: [110, 120]

Thorough Explanation Of Similar Problem Here!

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