Given the constant matrix
A= \begin{bmatrix}4&-1&0\\3&1&-1\\1&0&1\end{bmatrix}
find the fundamental matrix for the system $y'=Ay$.
After attempting to solve the system, I ended up with a general solution of the form,
$y(t) = C_1e^{2t}u + C_2e^{2t}v + C_3e^{2t}$
where u= \begin{bmatrix}1\\2\\1\end{bmatrix}
v=\begin{bmatrix}2+t\\3+2t\\1+t\end{bmatrix}
and w= \begin{bmatrix}\frac{t^2}{2}+2t+2\\t^2+3t+2\\\frac{t^2}{2}+t+1\end{bmatrix}
could I get some feedback on this answer? Is it correct?
P.S. the $\frac{t^2}{2!}$ comes from generalizing the eigenvector, since it has an eigenvalue of 2, with multiplicity 3.