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GATE ECE 2007 | Question-81

Statement for Linked Answer Questions 80 & 81:
Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\left[\begin{array}{r}1 \\ -2\end{array}\right]$, then the system response is $\mathbf{x}(t)=\left[\begin{array}{r}e^{-2 t} \\ -2 e^{-2 t}\end{array}\right]$
If the initial state vector of the system changes to $x(0)=\left[\begin{array}{r}1 \\ -1\end{array}\right]$, then the system response becomes $\mathbf{x}(t)=\left[\begin{array}{c}e^{-t} \\ -e^{-t}\end{array}\right]$.


The system matrix $\mathbf{A}$ is

  1. $\left[\begin{array}{rr}0 & 1 \\ -1 & 1\end{array}\right]$
  2. $\left[\begin{array}{rr}1 & 1 \\ -1 & -2\end{array}\right]$
  3. $\left[\begin{array}{rr}2 & 1 \\ -1 & -1\end{array}\right]$
  4. $\left[\begin{array}{rr}0 & 1 \\ -2 & -3\end{array}\right]$
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