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Linear equation

  1. Sep 11, 2011 #1
    Let a be a fixed nonzero vector in R^n

    a. Show that the set S of all vectors x such at ax=0 is a subspace of R^n.
    b. show that if k is a nonzero real number, then the set A of all vectors x such that ax=k is an affine subspace of R^n, but not a linear subspace.

    how do i even show this.. im so confused. help please!! thanks.
    Last edited: Sep 11, 2011
  2. jcsd
  3. Sep 11, 2011 #2


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    Try?? Pretty please? Tell me what you might need to prove S is a subspace. You can look it up in the book if you want to. What's the definition of a subspace?
  4. Sep 11, 2011 #3
    i know that S needs to be closed under addition and numerical multiplication.. im just not sure how to show this?!
  5. Sep 11, 2011 #4


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    If x1 is in S then a.x1=0. If x2 is in S then a.x2=0. (I'm using '.' for dot product). Can you give me some reason why that would mean x1+x2 is in S? What would you have show to prove x1+x2 is in S? That would give you closure under addition.
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