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The state variable formulation of a system is given as

$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$  ,  $x_1(0)=0$  ,  $x_2(0)=0$ and $y=\begin{bmatrix} 1 & 0 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}$

The response $y (t)$ to a unit step input is

  1. $\frac{1}{2}-\frac{1}{2}e^{-2t}$
  2. $1-\frac{1}{2}e^{-2t}-\frac{1}{2}e^{-t}$
  3. $e^{-2t}-e^{-t}$
  4. $1-e^{-t}$
in Linear Algebra by (1.5k points)
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