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Subspace in R^3

  1. Oct 22, 2007 #1
    Let A be a fixed 2x3 matrix. Prove that the set
    [itex]W={x \in R^{3} :Ax=[^{1}_{2}]} [/itex] (2x1 matrix 1 on top 2 at the bottom)

    what does the information after the ":" mean? is it a condition?
    I dont understand this problem. Can anyone help me out?
    Last edited by a moderator: Mar 10, 2013
  2. jcsd
  3. Oct 22, 2007 #2


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    Yes, it is a condition. You're trying to prove if this set of vectors x such that the condition after ":" holds is a subspace of R^3, I guess? You didn't completely lay out the problem, btw.
  4. Oct 22, 2007 #3


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    Ok, this is how set notation works.

    If I say...

    A = { x : x e N }

    Then that read... x is an element of A if x is an element N (the natural numbers). Hence, A = N, right? Do you agree?

    Let's think of something a little harder...

    A = { (x,y) : x + y = 1, and x,y e Z }

    Z is all the integers including 0. So, what's in A? Well, all (x,y) are elements of A if x+y=1 and x,y element of Z. An example is (0,1) because 0+1 = 1 and 0 e Z and 1 e Z.

    Anyways, now go back and re-read that question and state it correctly. And look for the Theorem on how to show a set is a subspace.
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