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Math Help - Matrix Product

  1. #1
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    Matrix Product

    Show that the jth column of the matrix product AB is equal to the matrix product ABj, where Bj is the jth column of B.


    I know this is true, but I'm not sure how to show it. Could someone please help me out? TIA!!!
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    Quote Originally Posted by TreeMoney View Post
    Show that the jth column of the matrix product AB is equal to the matrix product ABj, where Bj is the jth column of B.


    I know this is true, but I'm not sure how to show it. Could someone please help me out? TIA!!!
    I would consider this to be more of a definition than something that needs to be proved.

    Let [A_{ij}] and [B_{jk}] be your matrices.

    Then by the definition of matrix multiplication:
    C_{mn} \equiv \sum_{j} A_{mj}B_{jn}

    So the jth column vector in C is C_j = AB_j by definition.

    -Dan
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