An industrial system with three industries has the input-output matrix D and external demand matrix E below. Solve for the output matrix X in the equation X = DX + E. D=begin{bmatrix}0.1 & 0.3&0.2 0.0 & 0.2&0.30.4&0.1&0.1 end{bmatrix} text{ and } E=begin{bmatrix}3000 35008500 end{bmatrix}

Globokim8 2021-02-14 Answered
An industrial system with three industries has the input-output matrix D and external demand matrix E below. Solve for the output matrix X in the equation
X = DX + E.
D=[0.10.30.20.00.20.30.40.10.1] and E=[300035008500]
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Expert Answer

2abehn
Answered 2021-02-15 Author has 88 answers
Step 1
Given:
The equation X=DX+E
and the matrices:
D=[0.10.30.20.00.20.30.40.10.1] and E=[300035008500]
Step 2
To solve the equation
X=DX+E
Subtract DX from both sides
X-DX=E
(ID)X=E
Pre-multiply both sides by (ID)1
X=(ID)1E(1)
Step 3
To simplify further, compute the matrix (I-D), and then its
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Jeffrey Jordon
Answered 2022-01-29 Author has 2064 answers

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