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Matrix equation

  1. Mar 7, 2007 #1
    Is it possible to put these three equations into a matrix equation

    w*a = b -2a + e
    w*b = c -2b + a
    w*c = d -2c + b

    of the style w*u = T*u where u is a vector, u = {a, b, c} and T is a matrix. w is just a number.
     
  2. jcsd
  3. Mar 7, 2007 #2

    mathman

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    Science Advisor
    Gold Member

    What are d and e? If they are really different and not typos, then you will need T*u+v=w*u, where v is the vector (e,0,d) and ------------------------------------------------
    ------------------------------------------------------------------
    T=
    -2 1 0
    1 -2 1
    0 1 -2
    --------------------------------------------------------------------------------
     
    Last edited: Mar 7, 2007
  4. Mar 7, 2007 #3
    no they are not typos, could I not use

    T = -2 1 e/c
    1 -2 1
    d/a 1 -2

    or is that just stupid?
     
  5. Mar 7, 2007 #4

    radou

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    Homework Helper

    What exactly are the unknowns in your equations? a, b, c? If so, then

    (2 + w)a - b = e
    -a + (2 + w)b - c = 0
    -b + (2 + w)c = d ,

    which can be written as
    [tex]\left(\begin{array}{ccc}2+w & -1 & 0\\-1 & 2+w & -1\\0 & -1 & 2+w\end{array}\right) \left(\begin{array}{ccc}a \\b\\c\end{array}\right)=\left(\begin{array}{ccc}e \\0\\d\end{array}\right)[/tex].
     
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