Simple eigenvalue problem (x'=[2x2]x)

Hi, I've got a homework problem that should be very simple, the previous problem was identical (different numbers) and was a breeze, but this one is giving me problems. Here's what we're asked for:

Apply the eigenvalue method to find the particular solution to the system of differential equations

which satifies the initial conditions

So I begin by finding the eigenvalues from the characteristic equation:

To get the matrices:

and

To get

and

Which gives the particular solution

But at this point, no values for a and/or b will satisfy

Can anyone help me out, please?

Thanks!