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Write the system in equation form?

  1. Nov 9, 2004 #1
    Hi, I'm given a matrix and I need to write it in equation form so that I will have three equations, using x(t), y(t), and z(t)

    The matrix is a 3x3
    [3 -2 0]
    x'= [-1 3 -2] *x
    [0 -1 3]

    I know how to rewrite it using only x(t) but I'm not sure how to do it using y(t) and z(t).

    thanks!
     
  2. jcsd
  3. Nov 9, 2004 #2

    HallsofIvy

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    Science Advisor

    Your problem may be that you are using " x(t)" in two different ways- as a vector function and as a component of the vector. Your
    [3 -2 1]
    [-1 3 2] x
    [0 -1 3]

    is the same as

    [3 -2 1][x(t)]
    [-1 3 2][y(t)]
    [0 -1 3][z(t)]

    Do the matrix multiplication: that's
    [3x(t)- 2y(t)+ z(t)]
    [-x(t)+ 3y(t)+2z(t)]
    [0x(t)- y(t)+3z(t)]

    so your system of differential equations is x'(t)= 3x(t)- 2y(t)+ z(t),
    y'(t)= -x(t)+ 3y(t)+ 2z(t), and z'(t) -y(t)+ 3z(t).
     
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