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GATE ECE 2006 | Question-59

A linear system is described by the following state equation
$$X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc}
0 & 1 \\ -1 & 0\end{array}\right]$$
The state-transition matrix of the system is

  1. $\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]$
  2. $\left[\begin{array}{cc}-\cos t & \sin t \\ -\sin t & -\cos t\end{array}\right]$
  3. $\left[\begin{array}{cc}-\cos t & -\sin t \\ -\sin t & \cos t\end{array}\right]$
  4. $\left[\begin{array}{cc}\cos t & -\sin t \\ \cos t & \sin t\end{array}\right]$
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