I have been given

dx/dt= -2 6
-3 4

I need to calculate the egien vectors and values

Write down the real general solution

Sofar i have
Eigen values as 1+3i, 1-3i
Eigen vectors as (1,0.5-0.5i) and (1,0.5+0.5i)

Are these correct?

and my real general solution as: e^t(A cos 3t + Bsin3t
A cos 3t + B sin3t-Asin3t+ Bcos 3t)

With A being alpha
and B being -3 beta