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Math Help - Subspaces

  1. #1
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    Subspaces

    Consider two subspaces V and W or R^n.

    1) Is the intersection V intersect W necessarily a subspace of R^n?

    2) Is the union V union W necessarily a subspace of R^n?
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  2. #2
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    Intersection yes - you can formally prove it by checking that the intersection set of V,W satisfies all the axioms of vector space

    Union no - as a counter example x-axis and y-axis are subspaces of R^2. yet the union of two i.e. co-ordinate axis is not a sub-space. infact it should be good to try what further condition should be imposed on V,W so that the union is a vector space. it is pretty trivial
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