Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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).

  2. jcsd
  3. Nov 9, 2004 #2


    User Avatar
    Staff Emeritus
    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).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Write the system in equation form?
  1. System of Equations (Replies: 1)

  2. System of equations (Replies: 1)