Okay thank you that cleared up how I'm using it wrt the input.
The results this gives me are the same as following Alec's suggestion below, as he pointed out they should. Unfortunately these results, while within the bounds of physics, are extraordinarily unlikely and there's always rectified results regardless of the data set I use, so I'm quite certain that this approach isn't going to work at all. I fear my linear alg skills are insufficient for this; I think this is an ill-conditioned system but I haven't figured out how to check for that with a m x n matrix instead of an m x m one.
Thanks for your help everyone. Case closed for now.

Okay thank you that cleared up how I'm using it wrt the input.
The results this gives me are the same as following Alec's suggestion below, as he pointed out they should. Unfortunately these results, while within the bounds of physics, are extraordinarily unlikely and there's always rectified results regardless of the data set I use, so I'm quite certain that this approach isn't going to work at all. I fear my linear alg skills are insufficient for this; I think this is an ill-conditioned system but I haven't figured out how to check for that with a m x n matrix instead of an m x m one.
Thanks for your help everyone. Case closed for now.

Thank you, this seems to be getting me closer to my goal, but I'm having some problems with the input and output, probably because I am having trouble translating the cryptic instructions and examples in MapleHelp into something that has relevance to the real world.
So continuing from the code block I have in the original post (though I changed B and s to Vector because they should've been that in the first place) I now have for my solution statement:
`Optimization[LSSolve]([B,A], assume=nonnegative);`

This returns a result without an error (finally) but the values are again not properly constrained. I am unable to glean any meaning from the instructions in Maple Help on how to provide a constraint matrix to the Optimization package (using matrix form). Two of my variables (sigma 1 and sigma 4) always come back as = zero regardless of the data set I use, so I suspect I'm not doing something right.
Again with regards to the input, I'm also not sure that what LSSolve is solving is actually what I want solved. Superficially it looks good, but between the cryptic function instructions and my rusty linear alg skills, I can't be sure.
So let me rephrase exactly what my data looks like. I have 1 Matrix (A, 14 x 4) and 1 Vector (B, 14) containing knowns. My unknowns (sigma, which I'll denote as 's' below) are 4 in number. Each row is basically of this form, where i = row number:
A(i,1) * s1 + A(i,2) * s2 + A(i,3) * s3 + A(i,4) * s4 = B(i)
So A(i,j) and B(i) are all known constants with *unknown* amounts of error, and there are 14 rows. s1, s2, s3, s4 are my four unknowns, and I know that their values **must** lie somewhere in the range of (5..500) and *probably* lie between (30..350).
So with that said, is LSSolve still the right method? Is there something more appropriate? Am I presenting the input in the right form?
Any suggestions at all would be appreciated.

Thank you, this seems to be getting me closer to my goal, but I'm having some problems with the input and output, probably because I am having trouble translating the cryptic instructions and examples in MapleHelp into something that has relevance to the real world.
So continuing from the code block I have in the original post (though I changed B and s to Vector because they should've been that in the first place) I now have for my solution statement:
`Optimization[LSSolve]([B,A], assume=nonnegative);`

This returns a result without an error (finally) but the values are again not properly constrained. I am unable to glean any meaning from the instructions in Maple Help on how to provide a constraint matrix to the Optimization package (using matrix form). Two of my variables (sigma 1 and sigma 4) always come back as = zero regardless of the data set I use, so I suspect I'm not doing something right.
Again with regards to the input, I'm also not sure that what LSSolve is solving is actually what I want solved. Superficially it looks good, but between the cryptic function instructions and my rusty linear alg skills, I can't be sure.
So let me rephrase exactly what my data looks like. I have 1 Matrix (A, 14 x 4) and 1 Vector (B, 14) containing knowns. My unknowns (sigma, which I'll denote as 's' below) are 4 in number. Each row is basically of this form, where i = row number:
A(i,1) * s1 + A(i,2) * s2 + A(i,3) * s3 + A(i,4) * s4 = B(i)
So A(i,j) and B(i) are all known constants with *unknown* amounts of error, and there are 14 rows. s1, s2, s3, s4 are my four unknowns, and I know that their values **must** lie somewhere in the range of (5..500) and *probably* lie between (30..350).
So with that said, is LSSolve still the right method? Is there something more appropriate? Am I presenting the input in the right form?
Any suggestions at all would be appreciated.

Hi Alec, thanks for taking the time to reply. Your responses adds some confusion to the matter though... does this mean that Maple 6 is incorrectly evaluating the solution? Because it arrives at 2 and 4 solutions respectively. It is especially confusing since the solution Maple is displaying for the second example is completely unphysical.

Hi Alec, thanks for taking the time to reply. Your responses adds some confusion to the matter though... does this mean that Maple 6 is incorrectly evaluating the solution? Because it arrives at 2 and 4 solutions respectively. It is especially confusing since the solution Maple is displaying for the second example is completely unphysical.