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Nonzero Matrcies A; B; C such that AC = BC and A does not equal B?

  1. Feb 13, 2014 #1

    sheldonrocks97

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    Gold Member

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

    Find nonzero matrices A; B; C such that AC = BC
    and A does not equal B

    2. Relevant equations

    None that I know about.

    3. The attempt at a solution

    I'm not sure where to start, I would like to know how to complete this problem.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 13, 2014 #2

    pasmith

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    Homework Helper

    The simplest non-zero matrices are
    [tex]
    \begin{pmatrix}
    1 & 0 \\ 0 & 0
    \end{pmatrix},\quad
    \begin{pmatrix}
    0 & 1 \\ 0 & 0
    \end{pmatrix},\quad
    \begin{pmatrix}
    0 & 0 \\ 1 & 0
    \end{pmatrix},\quad
    \begin{pmatrix}
    0 & 0 \\ 0 & 1
    \end{pmatrix}
    [/tex]
    Play around.
     
  4. Feb 13, 2014 #3
    If AC = BC, then AC - BC = 0. I.e. (A-B)C = 0.

    Can you find two non-zero matrices that multiply to zero?
     
  5. Feb 13, 2014 #4

    AlephZero

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    Science Advisor
    Homework Helper

    Find out about singular matrices.
     
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