I tried cancelling it down into a more silky and manageable matrix:
20b+20d=-700 (This can be cancelled to b+d=-35)
200b+40c+20d-140a=-13800 <------This equation has too many variables.
We now have:
In matrix form this is:
The next step is finding the determinant:
(I would write down how I got these numbers, but even Microsoft Word Equation Drawer has it's limits!)
This is only a bit of the proof. Since the determinant=0, there is either no inverse (and hence no solutions) or all the points are mapped to a line and it has planes as solutions. None of the lines are multiples of each other so they're all different. It as been a while since i've done matrices so I can't actually remember if that has any significance. :s
I'm not really sure where else to go with this so I hope you (or another poster) can figure it out!