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A second-order linear time-invariant system is described by the following state equations

$$\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$$

$$\frac{d}{dt}x_2(t)+x_2(t)=u(t)$$

where $x_1(t)$ and $x_2(t)$ are the two state variables and $u(t)$ denotes the input. If the output $c(t)=x_1(t)$, then the system is

  1. controllable but not observable
  2. observable but not controllable
  3. both controllable and observable
  4. neither controllable nor observable
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