Problem with solve matrix
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Nguyen Tien Dung
on 5 Jul 2020
Commented: jose antonio valles
on 26 Nov 2021
Hi everyone,Can you help me solve this problem
clc
clear all
disp('An economic system composed of 3 sectors has the input-output matrix');
D=[0.5,0.1,0.1;0.2,0.5,0.3;0.1,0.3,0.4]
disp('The output vector X when the external demands are E');
E=[7900;3950;1975]
disp(['To meet the outside demand,the vector X must satisfy the Leontief equation:' ...
'X=DX+E =>(I-D)X=E=>X=((I-D)^(-1))E']);
I=[1,0,0;0,1,0;0,0,1]
X = [(I-D)^(-1)]*E
and X=(inv(I-D))*E
but all answer error and don't give right answer X=[27500;33750;24750]
2 Comments
Accepted Answer
Stephan
on 5 Jul 2020
For me your code works:
disp('An economic system composed of 3 sectors has the input-output matrix');
D=[0.5,0.1,0.1;0.2,0.5,0.3;0.1,0.3,0.4]
disp('The output vector X when the external demands are E');
E=[7900;3950;1975]
disp(['To meet the outside demand,the vector X must satisfy the Leontief equation:' ...
'X=DX+E =>(I-D)X=E=>X=((I-D)^(-1))E'])
I=[1,0,0;0,1,0;0,0,1]
X = ((I-D)^(-1))*E
X=(inv(I-D))*E
results in:
An economic system composed of 3 sectors has the input-output matrix
D =
0.5000 0.1000 0.1000
0.2000 0.5000 0.3000
0.1000 0.3000 0.4000
The output vector X when the external demands are E
E =
7900
3950
1975
To meet the outside demand,the vector X must satisfy the Leontief equation:X=DX+E =>(I-D)X=E=>X=((I-D)^(-1))E
I =
1 0 0
0 1 0
0 0 1
X =
1.0e+04 *
2.7500
3.3750
2.4750
X =
1.0e+04 *
2.7500
3.3750
2.4750
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