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An unforced linear time invariant (LTI) system is represented by $$\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0& -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$$ If the initial conditions are $x_1(0)= 1$ and $x_2(0)= -1$, the solution of the state equation is

  1. $x_{1}(t)= -1, \:  x_{2}(t)= 2$
  2. $x_{1}(t)= -e^{-t}, \: x_{2}(t)= 2e^{-t}$
  3. $x_{1}(t)= e^{-t}, \: x_{2}(t)= -e^{-2t}$
  4. $x_{1}(t)= -e^{-t}, \: x_{2}(t)= -2e^{-t}$
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