1. Limited time only! Sign up for a free 30min personal 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!

Matrix Differential Equation

  1. Feb 17, 2012 #1
    1. The problem statement, all variables and given/known data
    The questions are in the image

    3. The attempt at a solution
    My solutions are
    V1=3*(1 -2)e-2t+ (-2) (1 -3)e-3t
    V2=1*(1 -2)e-2t+ (-1) (1 -3)e-3t

    How do I get the X matrix since my solutions are in exponential still.

    Thank you for all the help
     

    Attached Files:

    Last edited: Feb 17, 2012
  2. jcsd
  3. Feb 18, 2012 #2
    According to your solution,
    [tex]X=(v_1\ v_2)=\begin{pmatrix}3e^{-2t}-2e^{-3t}&-6e^{-2t}+6e^{-3t}\\
    e^{-2t}-e^{-3t}&-2e^{-2t}+3e^{-3t}\end{pmatrix}.[/tex]
     
  4. Feb 18, 2012 #3
    That means I just plug in t=0 to prove that x(0)=(1 0
    0 1) and also use the same method to prove that dx/dt =AX
     
    Last edited: Feb 18, 2012
  5. Feb 18, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You have the columns and rows swapped.
     
  6. Feb 18, 2012 #5
    Even after multiplying it I get this respective solutions, what do I do next?
     

    Attached Files:

  7. Feb 18, 2012 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You can write v1 as a single vector:
    $$\vec{v}_1 = \begin{pmatrix} 3e^{-2t} - 2e^{-3t} \\ -6e^{-2t} + 6e^{-3t}\end{pmatrix}$$Do the same for ##\vec{v}_2##.
     
  8. Feb 18, 2012 #7
    i get that part but after that what do I do to get just numbers in my 2x2 matrix so that I can prove dx/dt =AX and x(0)= \begin{pmatrix}1 0\\ 0 1\end{pmatrix}
     
  9. Feb 18, 2012 #8

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Like the problem says, the first column of X is v1. Its second column is v2. It's not going to be just numbers. I'm not sure why you think it has to be.
     
  10. Feb 18, 2012 #9
    Okay but then if I put t=0 into the x equation, I do not get the identity matrix and how would I verify that dx/dt=AX by just differentiating the X matrix?.

    Thank you for all the help
     
  11. Feb 18, 2012 #10

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Show us how you're calculating X when t=0.
     
  12. Feb 18, 2012 #11
    Okay I got just did a arithmetic error, but how do I verify that dx/dt=AX
     
  13. Feb 18, 2012 #12

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Calculate both sides and show they're equal to each other.
     
  14. Feb 18, 2012 #13
    Okay I will give it a try, thank you very much for all the help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook