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Question

# Determine the general solution to the linear system$\mathbf { x } ^ { \prime } = A \mathbf { x }$for the given matrix A.$\left[ \begin{array} { r r } { 3 } & { 13 } \\ { - 1 } & { - 3 } \end{array} \right].$

Solution

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Step 1
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We are given the matrix

\begin{aligned} A=\begin{bmatrix} & 2 & 13 &\\ & -1 & -3 & \end{bmatrix}. \end{aligned}

Our task is to find the general solution to the system ${\bf x}'=A{\bf x}$.

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