1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exp Matrix to solve an initial value problem

  1. Sep 23, 2008 #1
    Exp Matrix to solve an initial value problem(urgent)

    1. The problem statement, all variables and given/known data

    Given the matrix [tex]A = \left[\[\begin{array}{ccc} 2 & 2 \\ 1& 3 \end{array}\right][/tex]

    a) Find the [tex]e^{tA}[/tex]

    2) Solve the [tex]x' = Ax + (1,0) \begin{array}{c} \end{array}[/tex] where x(0) = (0,0)

    3. The attempt at a solution

    a) [tex]e^{tA} = P_{A} \cdot e^{Dt} \cdot P'[/tex]

    Which in my book gives

    [tex]e^{tA} = \left[\[\begin{array}{ccc} -2 & 1 \\ 1& 1 \end{array}\right] \cdot \left[\[\begin{array}{ccc} e^{t} & 0 \\ 0& e^{16t} \end{array}\right] \cdot \left[\[\begin{array}{ccc} -\frac{1}{3} & \frac{1}{3} \\ \frac{4}{3}& \frac{8}{3} \end{array}\right] [/tex]

    [tex]e^{tA} = \left[\[\begin{array}{ccc} \frac{2}{3}\cdot e^{t} + \frac{4}{3}\cdot e^{16t} & \frac{-2}{3}\cdot e^{t} + \frac{8}{3}\cdot e^{16t} \\ \frac{-1}{3}\cdot e^{t} + \frac{4}{3}\cdot e^{16t} & \frac{1}{3}\cdot e^{t} + \frac{8}{3}\cdot e^{16t} \end{array} \right][/tex]

    Doesn't that look okay??

    b) From what I remember the solution for x' can be written as [tex]X = e^{tA} \cdot C[/tex]

    Which in my case gives [tex]X = e^{tA} \cdot \left[\begin{array}{c} 0 \\ 0 \end{array} \right][/tex]

    This is how my textbook argues how solve such eqn, but if I fry to x' I totally different result. What am I doing wrong??? Or could somebody please be so kind to lead me on the right path/track?? :)

    Sincerely
    Alphaboy
     
    Last edited: Sep 23, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Exp Matrix to solve an initial value problem
  1. Matrix Question (Replies: 0)

  2. Vandermonde matrix (Replies: 0)

Loading...