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Is there more than one way to prove this?

  1. Sep 23, 2012 #1
    Suppose that A is an n × n matrix and u and v
    are vectors in R^n. Show that if Au = Av and
    u ≠ v, then A is not invertible.


    This is the book's proof:
    From the fact that Au = Av, we have A(u − v) = 0. If
    A is invertible, then u − v = 0, that is, u = v, which
    contradicts the statement that u = v.

    Mine proof is, if A is invertible thus A^-1 exists
    (A^-1)(Au)=(A^-1)(Av)
    A^-1*A=I
    →u=v
    if u≠v then then the above does not hold, implying that A^-1 does not exist.
     
  2. jcsd
  3. Sep 23, 2012 #2

    gabbagabbahey

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    Gold Member

    Your proof looks fine to me :approve:
     
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