solve y'=Ay+b system of equation where

$\displaystyle \vec{A}=\begin{pmatrix}3 & 1 & 0\\-1 & 1 & 0\\ 1& 1 &2\end{pmatrix},\vec{B}=\begin{pmatrix}e^{2x}\\ 0\\ e^{2x}\end{pmatrix}$

i cant see where is my mistake in my method

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