consider v={(x,y) :xy=0 } with the usual vector addition and scalar multiplication in R^2 is (v,+,.) a vector space?

1 Answer

  • No; V is not closed under vector addition.

    To see this, note that both (1,0) and (0,1) are in V (since the product of their components equal 0), but their sum (1,0) + (0,1) = (1,1) is not in V because 1 * 1 is nonzero.

    I hope this helps!

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