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Homework Help: Injections and Surjections

  1. Sep 23, 2010 #1
    I'm having a lot of trouble figuring out how to do this proof:

    Given real numbers a, b, c, d, let f: real^2 ----> real^2 be defined by f(x, y) = (ax + by, cx + dy). Prove that f is injective if and only if f is surjective.

    If anybody could help, that would be great.
  2. jcsd
  3. Sep 23, 2010 #2


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    Do you know what the rank-nullity theorem is?
  4. Sep 23, 2010 #3
    A quick google search reveals that it appears to be dealing with some linear algebra I don't quite understand...

    My book gives me the following hint for this proof: Consider two cases, depending on whether ad - bc = 0.

    Not sure if that helps, I'm pretty confused here.
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