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Let U and w be two subspaces of the same vector space V.Is U union W necessarily a vector space?

Sezer Akbay
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    http://math.stackexchange.com/questions/71872/union-of-two-vector-subspaces-not-a-subspace – symplectomorphic Jan 14 '16 at 05:27
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    the answer is no, and it's almost impossible not to understand why if you think of a simple example. moreover, this question is a duplicate; it's asked dozens of times on this site. show a little effort. – symplectomorphic Jan 14 '16 at 05:28
  • Name a 1-dimensional vector space of $\Bbb R^2$. Name another. Is their union a vector space? – BrianO Jan 14 '16 at 05:33

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Let $V = R^3$. Choose the subspaces to be generated by two non parallel vectors, respectively. Then the sum of the two vectors is not contained in the union.

Henricus V.
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