EDIT: just writing out my working. 2 mins .

http://www.wolframalpha.com/input/?i=eigenvalues+{{1%2C+1%2C+1}%2C{2%2C2%2C+2}%2C+{3 %2C+3%2C+3}}

How is {1, 2, 3} and answer(Corresponding to EV = 6)? I get {2, 1, 0) and just can't seem to work out how they get (1, 2, 3)!

Eigen Value 6:

So, for

I obtain:

I obtain:

...And actually just typing this out i've mega confused myself as there are now 4 different basis and there's meant to be a max of 3 :S.