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Question about Multiplying Matrices

  1. Apr 3, 2012 #1
    Is it ok to reduce the two matrices through row operations first before multiplying them together or will the answer no longer be row equivalent?

    Thanks for any input!
  2. jcsd
  3. Apr 3, 2012 #2


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    Staff Emeritus
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    Reducing a matrix through row operations is the same as multiplying the matrix by the elementary matrices corresponding to each row operation (the elementary matrix corresponding to a given row operation is the matrix you get by applying that row operation to the identity matrix). That is, if matrix A can be reduced to A' by row operations corresponding to elementary matrices d1, d2... dn and B can be reduced to B' by row operations corresponding to elementary matrices e1, e2, ..., e[sun]m[/sub], then A'= d1d2...dnA and B'= e1e2...emB so that A'B'= d1d2...dnAe1e2...emB which is, generally, NOT the same as AB.
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