I'm not a numerical analysis expert, but if the matrix is "near singular", then the matrix is what is called "ill-conditioned" and it's determinant is very close to zero, so "all bets are off".
We can check how well it would invert:
cond(M0)
gives about
4e18
As a rule of thumb, a condition number of 10^k indicates that you will loose about k digits in precision, which in this case is very bad. See http://en.wikipedia.org/wiki/Condition_number.
This means that the matrix will introduce large errors when you do any kind of calculations with it, such as an inverse. I found this which might help you: http://www.mathworks.se/matlabcentral/newsreader/view_thread/67650 In the link, they mention the use of "psuedo inverse" pinv(), you should check it out.
