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Math Help - Finding nonzero matrices that result in AB=0

  1. #1
    DrZ
    DrZ is offline
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    Finding nonzero matrices that result in AB=0

    This question has confused me a bit.

    Find nonzero 2x2 matrices A and B such that AB=0.

    I've been just trying to find two 2x2 matrices who result in a 2x2 matrix with 0 at each position.

    The answer I got is

    A =
    1 1
    1 1

    B=

    1 1
    -1-1

    so AB =
    0 0
    0 0

    I think that is correct, but the question ased for AB=0, does that mean a matrix with 0 in all positions?
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  2. #2
    Super Member TheChaz's Avatar
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    Quote Originally Posted by DrZ View Post
    This question has confused me a bit.

    Find nonzero 2x2 matrices A and B such that AB=0.

    I've been just trying to find two 2x2 matrices who result in a 2x2 matrix with 0 at each position.

    The answer I got is

    A =
    1 1
    1 1

    B=

    1 1
    -1-1

    so AB =
    0 0
    0 0

    I think that is correct, but the question ased for AB=0, does that mean a matrix with 0 in all positions?
    It DOES mean a matrix with zero in all positions!
    How about
    1 0
    0 0

    and

    0 1
    0 0 ??
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  3. #3
    MHF Contributor
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    The OP's example also works.
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  4. #4
    Super Member TheChaz's Avatar
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    Quote Originally Posted by emakarov View Post
    The OP's example also works.
    Of course. I guess it's worth mentioning that "0" in the context of a matrix product means the zero matrix.
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