Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar

    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


    User Avatar
    Science Advisor

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook