2
$\begingroup$

I want to determine a balance distribution.

Ü = {{0.4, 0.2, 0.3}, {0.3, 0.5, 0.2}, {0.3, 0.3, 0.5}}; 

and

X = {{x1}, {x2}, {x3}}; 

so that

Ü.X == X

But when I want to solve

Solve[{0.4 x1 + 0.2 x2 + 0.3 x3 == x1,0.3 x1 + 0.5 x2 + 0.2 x3 == x2, 0.3 x1 + 0.3 x2 + 0.5 x3 == x3,
   x1 + x2 + x3 == 240000}, {x1, x2, x3}]

I get the error

RowReduce::luc: Result for RowReduce of badly conditioned matrix {{0.3, 0.2, -0.6, 0.}, {0.2, -0.5, 0.3,0.}, {-0.5, 0.3, 0.3, 0.}, {1., 1., 1., -240000.}} may contain significant numerical errors. >>
{}

How can I solve this system?

$\endgroup$
4
$\begingroup$

The proximate cause of the message is that the matrix I-U has determinant 10^(-17) and hence the linear system (I-U).x=0 cannot be solved easily in such a direct manner. As J. M. suggests, you can solve for the eigenvalues and eigenvectors without trouble. In this case

Eigensystem[U]

shows three eigenvalues (1, 0.2, and 0.2) and the three corresponding vectors x. For instance, the eigenvector corresponding to the unit eigenvalue is

{0.511834, 0.565711, 0.646527}

so you can solve c*(0.511834 + 0.565711 + 0.646527)=240000 for c and you will have your desired x.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.