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Homework Help: AB=0 but A and B different from 0

  1. Sep 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Need to show that if A is not invertible then exist B (nxn) such that AB=0 but B is different from 0.

    2. Relevant equations

    3. The attempt at a solution
    Thought about writing A like E1...Ek*R where Ei are elementary matrices and R(different from I) the row reduced echelon matrice but doesnt seem.to help, any idea??
  2. jcsd
  3. Sep 29, 2015 #2
    Hint: a nontrivial linear combination of the columns/rows of ##A## is zero.
  4. Sep 29, 2015 #3


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    Science Advisor
    Gold Member

    Similar to Micromass, write the columns so that they are in the " necessary ( and non-trivial) " kernel.
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