I tried cancelling it down into a more silky and manageable matrix:

200b+152c+20d+7(2300-20a-16c)=-2300

16a+152b+168c=1800

20b+20d=-700 (This can be cancelled to b+d=-35)

4a+28b+8(2300-20a-16c)=500

200b+40c+20d-140a=-13800 <------This equation has too many variables.

152b+168c+16a=1800

20b+20d=-700

28b-128c-156a=-17900

200b+40c+(-700-20b)-140a=-13800

180b+40c-140a=-13100<------much better!

We now have:

180b+40c-140a=-13100

152b+168c+16a=-700

28b-128c-156a=-17900

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!)

2723840+17920-4717440+948480+658560+368640=0

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!