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Question

# Find the general solution of the system of differential equations.\begin{align*} y_1'&=2y_1\\ y_2'&=3y_1+2y_2+3y_3\\ y_3'&=-3y_1-y_3 \end{align*}

Solution

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$\bold{y}=\begin{bmatrix} y_1 \\ y_2\\ y_3\end{bmatrix}$

and

$A=\begin{bmatrix} 2 & 0 & 0 \\ 3 & 2 & 3 \\ -3 & 0 & -1 \end{bmatrix}$

Let $\bold{y}$ contain the variables and $A$ the matrix containing the coefficients of the variables in the system of equations.

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