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Is this a subspace of R^4

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Is this a subspace of R^4, (2x+3y, x, 0 , 1) . Give reasons

    2. Relevant equations



    3. The attempt at a solution

    I am completely stuck at this one
     
  2. jcsd
  3. Mar 25, 2012 #2
    A subset U of V is a subspace of V if it satisfies the properties needed to be a vector space: additive identity; closure under vector addition; closure under scalar multiplication.

    Check that your given subset satisfies the properties.

    a) Is there an additive identity from your set for R^4?

    b) If you take two vectors from your given space, a and b, is a+b still in your set?

    c) Is the scalar multiple of any vector in your set still in the set?
     
    Last edited: Mar 26, 2012
  4. Mar 26, 2012 #3

    HallsofIvy

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    You might want to look particularly at the fourth component in a scalar product such as 2v.
     
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