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Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for this system is

  1. $x(t) = \begin{bmatrix}e^{-t} & te^{-2t} \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1  \\1\end{bmatrix}$
  2. $x(t) = \begin{bmatrix}e^{-t} & 0 \\0 & e^{2t}\end{bmatrix}$ $\begin{bmatrix}1  \\1\end{bmatrix}$
  3. $x(t) = \begin{bmatrix}e^{-t} & -t^2e^{-2t} \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1  \\1\end{bmatrix}$
  4. $x(t) = \begin{bmatrix}e^{-t} & 0 \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1  \\1\end{bmatrix}$
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