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Dividing polynomial matrices

  1. Jul 31, 2011 #1

    syj

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    1. The problem statement, all variables and given/known data

    Divide

    A(x)=
    [x3+2x2+3 -4x3-x2-5]

    [3x2-2 x3-2x2+x+4]

    by

    B(x) =
    [x+4 -3]
    [-x+6 x+2]

    on both the right side and the left side.


    2. Relevant equations



    3. The attempt at a solution

    I am thinking i need to rewrite A(x) as:

    [1 -4]
    [0 1 ] x3 +


    [2 -1]
    [3 -2]x2+

    [0 0]
    [0 1]x +

    [3 -5]
    [-2 4]
    and do the same to B(x)

    but i don't know what to do from there. :(
     
  2. jcsd
  3. Aug 1, 2011 #2

    lanedance

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    Homework Helper

    ok so do you mean
    [tex] A(x) = \begin{pmatrix}
    x^3+2x^2+3 & -4x^3-x^2-5\\
    3x^2-2 & x^3-2x^2+x+4
    \end{pmatrix}
    [/tex]

    i have to admit I don't really understand the question. What do you mean by divide? The matrix equivalent would be to multiply by the inverse, assuming it exists

    It me help to write B as
    [tex]
    B = M\begin{pmatrix}
    x\\
    1
    \end{pmatrix}
    [/tex]

    Then can you show, assuming x is not zero, that the inverse is
    [tex]
    B^{-1} =
    \begin{pmatrix}
    \frac{1}{x} &
    1
    \end{pmatrix}
    M
    [/tex]
     
    Last edited: Aug 1, 2011
  4. Aug 1, 2011 #3

    syj

    User Avatar

    thanks
    i found a book online that explained the method.
    except in the book they referred to the matrix as a lambda matrix not a polynomial matrix.
    thanks again for all the help.
    i shall be posting more questions soon ;)
     
  5. Aug 1, 2011 #4

    lanedance

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    Homework Helper

    no worries, made a correction above, so if you were using it re-check
     
  6. Aug 1, 2011 #5

    lanedance

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    Homework Helper

    ok yeah I've haven't seen lambda matricies before, this is a good intro after a google
    http://solitaryroad.com/c152.html
     
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