MHB Find Sample Solutions for Underdetermined Systems of Linear Equations

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A user seeks a tool to generate non-negative solutions for a system of 379 linear equations with 6325 unknowns. Suggestions include computing the basis of the nullspace of the corresponding matrix and selecting arbitrary elements while enforcing non-negativity. While no online tool is confirmed to handle such a large matrix, free linear algebra software may be available. Mathematica is mentioned as a capable option, though it is not free. Exploring available software or seeking assistance from someone with access to Mathematica could be beneficial.
ztepman
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I have a system of 379 linear equations and 6325 unknowns. Does anyone know of a tool that can generate some (non-negative) solutions that satisfy this system? I know there are infinitely many, but it would be useful just to have a few for my purposes.
 
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Why not just compute the basis of the nullspace of the resulting matrix and pick arbitrary elements in that nullspace? Adding the condition that the coefficients should be nonnegative shouldn't be too hard to enforce I think.

I don't think any online tool that will let you feed it such a huge matrix but I am sure there exists free software to do it, maybe look around for free linear algebra software? Mathematica can do it but isn't free, but perhaps you know someone that has a copy that can run the data for you?
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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