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Can anyone explain why (linear algebra)

  1. Mar 2, 2008 #1
    Why for the subspaces V and W in R^n , the

    union of V and W is not a subspace of R^n?

    Thank you.
  2. jcsd
  3. Mar 2, 2008 #2


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    Look at some examples to see why such as the union of two lines through the origin in R^2.
  4. Mar 2, 2008 #3


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    Staff Emeritus
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    If v is in subspace V and w is in subspace W, it is not, in general, true that v+ w is in V[itex]\cup[/itex]W. You can give a specific counter example by using Vid's suggestion. Let V= {(x,y)| y= x}, v= (1, 1), W= {(x,y)|y= -x}, w= (-1, 1). Is v+ w in the union of V and W?
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