Need help with solving this system of ODE's?

[Dr. G]

y'=Ay where A is the matrix (its hard to type a matrix so hopefully this makes sense)
(-6, 1)
(0, -6)

I solved for the characteristic polynomial and get (x+6)(x+6)

So the eigenvalue is -6 with a multiplicity of 2.

Then to find the corresponding eigenvector, v, I take the null space of A+6(Identity matrix) but this is the null space of
(0, 1)
(0, 0)

Isn't that just (0, 0) - transpose ?

Then it has a trivial null space and then I can't find another vector w such that
(A+6(Identity matrix)) * w = v

So I can't find a solution.

Or is it that there is no solution?

Thanks!