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Differential Equations in Matrices

  1. Feb 16, 2013 #1
    Capture-2_zps0f870620.jpg

    I realize that Δ(s) is the cross product of the matrix on the left, but how did the solutions manual get the matrix on the far right multiplied by R_1(s) and R_2(s)? I need those matrix values to do the rest of the problem. Any help is appreciated, thank you.
     
  2. jcsd
  3. Feb 16, 2013 #2

    LCKurtz

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    They multiplied both sides of the first equation by the inverse of the matrix on the left to solve for ##Y_1(s)## and ##Y_2(s)##.
     
  4. Feb 16, 2013 #3

    SteamKing

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    I think Delta (s) is technically the determinant of the left most s matrix, rather than the cross product.
     
  5. Feb 17, 2013 #4
    I still don't see how they did it, sorry.
     
  6. Feb 17, 2013 #5

    LCKurtz

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    Do you know how to find the inverse of$$
    \begin{bmatrix}
    s(s+2) & 3\\
    3s+1 & s^2-1

    \end{bmatrix}$$If so, do that first. Then multiply it on the left of$$
    \begin{bmatrix}
    1 & 1\\
    s & 1
    \end{bmatrix}$$and see if that helps you.
     
  7. Feb 18, 2013 #6
    yup, thank you LCKurtz. That was the obvious answer. Now that I have a TI-nspire CAS, I can just type it in and it comes out
     
  8. Feb 18, 2013 #7

    D H

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    You don't need a calculator for this. Sometimes a calculator hinders learning.
     
  9. Feb 18, 2013 #8
    True, but that new CAS is awesome. I did the math by hand eventually, after many, many google searches on the right steps to take
     
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