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Math Help - Row space of a matrix?

  1. #1
    Junior Member
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    Row space of a matrix?

    How do I prove:

    row(A^2)\subset row(A), for a matrix A
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  2. #2
    Super Member
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    Thanks
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    each row of A^2 can be shown to be linear combination of rows of A. (look at the definition of matrix multiplication). Hence row space of A^2 is a subset of row space of A.

    Not sure if there is another more conceptual argument.
    Thanks
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