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2 non-zero matrix A and B, and A*B=0

  1. Apr 26, 2005 #1
    There are 2 non-zero matrix A and B, and A*B=0.
    another matrix C is a row equivalent to A.
    is C*B=0 ?
     
  2. jcsd
  3. Apr 26, 2005 #2
    Yes. Because C=E*A for some matrix E.
     
  4. Apr 26, 2005 #3

    mathwonk

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    actually this is the fundamental reasaon row equivalence is a useful notion in solving linear systems.

    i.e. this says exactly that any solutions of the equation AX=0, also solve CX=0.

    recall the use of row reduction in solving systems: you reduce A to an equivalent matrix such that CX=0 is easy to solve. then you announce that the solutions are also solutions of AX=0.
     
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