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Help whit a problem. (I have no idea)

  1. Dec 3, 2004 #1
    Calculate [itex] e^A [/itex] if [itex] A = \left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right) [/itex]

    Maybe using that [tex] e^x = \sum_{n=0}^\infty \frac{x^n}{n!} [/tex], then

    [tex] e^A = \sum_{n=0}^\infty \frac{\left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right)^n}{n!} [/tex]
    but i dont know if this is the right way for doing this. Please help me. Thanks.
     
  2. jcsd
  3. Dec 3, 2004 #2

    AKG

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    That's precisely it.
     
  4. Dec 3, 2004 #3
    Ok, thanks.
     
  5. Dec 4, 2004 #4

    HallsofIvy

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    Although you may have difficulty calculating [tex]\left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right)^n [/tex]
    Knowing that its eigenvalues are 1 and 2 (with eigenvectors <2, -1> and <1, -1> respectively) will help.
     
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