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Homework Help: Proving Linear System

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that there are no A,B (2x2 and real number matrices)

    such that AB-BA=I2

    2. Relevant equations

    N/A

    3. The attempt at a solution

    can anyone give me clue, how to prove this?
     
  2. jcsd
  3. Apr 11, 2010 #2
    Write down the full equation

    [tex]
    \left(
    \begin{array}{cc}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
    \end{array}
    \right)\left(
    \begin{array}{cc}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
    \end{array}
    \right)-\left(
    \begin{array}{cc}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
    \end{array}
    \right)\left(
    \begin{array}{cc}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
    \end{array}
    \right)=\left(
    \begin{array}{cc}
    1 & 0 \\
    0 & 1
    \end{array}
    \right)[/tex]

    After you do that it will be obvious
     
  4. Apr 11, 2010 #3
    i did, but then i get,

    [tex]\begin{pmatrix} bg-fc & af+bh+be+df \\ ce+dg-aq-ch & cf-bg \end{pmatrix}[/tex]

    assume that my

    a11=a
    a12=b
    .
    .
    .
    b21=g
    b22=h

    then? solve the equation right?
     
  5. Apr 11, 2010 #4
    owh wait,

    bg-fc=1

    cf-bg=1

    its contradiction..

    right?
     
  6. Apr 11, 2010 #5
    Yeah that's the idea I think
     
  7. Apr 11, 2010 #6
    hoho, that's proof alright,, thank you very much

    next, can you please check my next question i posted.. ^^
     
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