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GATE ECE 2008 | Question-27

Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$. The value of $\mathbf{e}^{\mathbf{P}}$ is

  1. $\left[\begin{array}{cc}2 e^{-2}-3 e^{-1} & e^{-1}-e^{-2} \\ 2 e^{-2}-2 e^{-1} & 5 e^{-2}-e^{-1}\end{array}\right]$
  2. $\left[\begin{array}{cc}e^{-1}+e^{-2} & 2 e^{-2}-e^{-1} \\ 2 e^{-1}-4 e^{-2} & 3 e^{-1}+2 e^{-2}\end{array}\right]$
  3. $\left[\begin{array}{cc}5 e^{-2}-e^{-1} & 3 e^{-1}-e^{-2} \\ 2 e^{-2}-6 e^{-1} & 4 e^{-2}+e^{-1}\end{array}\right]$
  4. $\left[\begin{array}{cc}2 e^{-1}-e^{-2} & e^{-1}-e^{-2} \\ -2 e^{-1}+2 e^{-2} & -e^{-1}+2 e^{-2}\end{array}\right]$
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