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Homework Help: Tricky Linear Mapping proof

  1. Sep 25, 2012 #1
    Hey guys, I was wondering if you could help me out with a question I've got, I really don't know where to go or really where to start! Here's the question:

    Let S be a subspace of a finite dimensional vector space V. Show that there exists a Linear Mapping L: V → V such that the kernel of L is S.

    I started off messing around with some examples and the theorem makes sense to me, I just can't figure out how to prove it! If someone could start me off that would be awesome.

  2. jcsd
  3. Sep 26, 2012 #2
    Take the orthogonal projection to the complement subspace of S.
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