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Homework Help: Linear algebra

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Let A be an m*p matrix whose columns all add to the same total say "s". Let B be a p*n matrix whose columns alladd to the same total say "t".Prove that the n columns of (AB) all sum to st.

    2. Relevant equations

    This is an obvious result but i am having trouble proving it with summation notation which is what we were told to do.

    A=∑(i=1 to m)a_{ij}

    B=∑(j=1 to p)b_{jk}

    (AB)=∑(j=1 to p)a_{ij}*b_{jk}

    But i am having trouble proving that each column sums to st even though i know this is the case.
  2. jcsd
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