Looking for a proof of non tractability (or perhaps a definition of tractable)  Given $C=XF$, and only data for $C$, solving for $X$ and $F$ has been described as not tractable (which I'm content to believe, but others aren't).  If that's the case, where does the following argument fall apart?
Suppose $C^i=XF^i$ is written:
$\begin{bmatrix}
  C_1^i \\\
  \vdots \\\
  C_m^i 
\end{bmatrix} = \begin{align}\begin{bmatrix}
  X_{1,1} & \dots & X_{1,n} \\\
  \vdots &  & \vdots \\\
  X_{m,1} & \dots & X_{m,n} 
\end{bmatrix}\end{align}\begin{bmatrix}
  F_1^i \\\
  \vdots \\\
  F_n^i 
\end{bmatrix}$
One instance of data for a given $i$ of $C^i$ would produce $m$ equations and $mn+n$ unknowns. 
$q$ instances of data for $C^i$ would produce $qm$ equations and $mn+qn$ unknowns.  
If the supposition that you need more equations than unknowns is sufficient, why can I contradict others statements of not tractability  by choosing whole number values to satisfy the inequality:  
$qm >= mn+qn$? 
Using say $q=6,m=3,n=2$.
 A: I don't think there's a general definition of tractability in the sense you probably mean, other than "unsolvable under the given conditions"; however "given conditions" are very important.
In practice conditions on a theorem aren't set beforehand but typically arise from working on the problem - you want to show X, but find out that X doesn't hold unless you also make assumption Y, and so then you ask yourself if Y is a reasonable thing to assume in the problem setting you are interested in. In the end you (hopefully) prove a theorem that has as few assumptions as you can get away with, and still is useful for the problem you are interested in.
Now, there is a clear distinction between the two situations "can I very likely get a practically satisfactory solution to (some impossible problem) if I add some extra constraints by applying domain knowledge" and "can I solve a problem that can be proved to be impossible in general". In your previous post, the problem you gave was impossible in general, but a good enough solution was tractable under mild assumptions. So, tractability is a function of how you choose to work on a problem, and specifically of which conditions or constraints you assume to hold/are happy to accept in the first place.
I can recommend Imre Lakatos's "Proofs and Refutations", which makes this point better than I could ever hope to and, IMHO, is one of those books that every intelligent person should read at sometime in their life. 
