Find the general solution to the system of differential equations

$$\begin{cases}

y'_1&=2y_1+y_2-y_3 \\y'_2&=3y_2+y_3\\y'_3&=3y_3

\end{cases}$$

ok I assume the next step is

$$\begin{bmatrix}

y'_1 \\y'_2 \\y'_3

\end{bmatrix}=\begin{bmatrix}

2 & 1 & -1 \\0 & 3 & 1 \\ 0 & 0 & 3

\end{bmatrix}

\begin{bmatrix}

y_1 \\y_2 \\y_3

\end{bmatrix}$$

I had this posted on another forum but think I was not starting out right so got no reply's