Problem with solve matrix

Question

Nguyen Tien Dung 2020-7-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/559787-problem-with-solve-matrix

评论： jose antonio valles 2021-11-26

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 个评论
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jose antonio valles 2021-11-26

and, this is you error

jose antonio valles 2021-11-26

and the last row is repeated "and X=(inv(I-D))*E"

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Answer 1

Stephan 2020-7-5

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/559787-problem-with-solve-matrix#answer_461276

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