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GATE ECE 2005 | Question-25

A linear system is equivalently represented by two sets of state equations.
\[\dot{X}=\mathrm{AX}+\mathrm{BU} \text { and } \dot{W}=\mathrm{CW}+\mathrm{DU} \text {. }\]
The eigenvalues of the representations are also computed as $\{\lambda\}$ and $\{\mu\}$. Which one of the following statements is true?

  1. $[\lambda]=[\mu]$ and $X=W$
  2. $[\lambda]=[\mu]$ and $X \neq W$
  3. $[\lambda] \neq[\mu]$ and $X=W$
  4. $[\lambda] \neq[\mu]$ and $X \neq W$
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