[7급 국가직 자동제어 2010년 9번]

1. ①
   $A=\left[\begin{array}{cc}0& 1\\ -2& -3\end{array}\right]$

   $\Phi (t)=\left[\begin{array}{cc}2e^{-t}-e^{-2t}& e^{-t}-e^{-2t}\\ -2e^{-t}+2e^{-2t}& -e^{-t}+2e^{-2t}\end{array}\right]$

   $\lambda =-1,-2$
2. ②
   $A=\left[\begin{array}{cc}0& 1\\ -3& -2\end{array}\right]$

   $\Phi (t)=\left[\begin{array}{cc}2e^{-t}-e^{-2t}& e^{-t}-e^{-2t}\\ -2e^{-t}+2e^{-2t}& -e^{-t}+2e^{-2t}\end{array}\right]$

   $\lambda =-2,-3$
3. ③
   $A=\left[\begin{array}{cc}0& 1\\ -2& -3\end{array}\right]$

   $\Phi (t)=\left[\begin{array}{cc}-2e^{-t}+2e^{-2t}& -e^{-t}+2e^{-2t}\\ 2e^{-t}-e^{-2t}& e^{-t}-e^{-2t}\end{array}\right]$

   $\lambda =-1,-2$
4. ④
   $A=\left[\begin{array}{cc}0& 1\\ -3& -2\end{array}\right]$

   $\Phi (t)=\left[\begin{array}{cc}-2e^{-t}+2e^{-2t}& -e^{-t}+2e^{-2t}\\ 2e^{-t}-e^{-2t}& e^{-t}-e^{-2t}\end{array}\right]$

   $\lambda =-2,-3$

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출처: 인사혁신처 공개 기출(공공데이터포털, 이용허락 제한 없음)