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Math Help - dimensional subspaces and direct sums

  1. #1
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    dimensional subspaces and direct sums

    1. Prove that if W_1 and W_2 are finite-dimensional subspaces of a vector space V, then the subspace W_1+ W_2 is finite-dimensional and dim( W_1+ W_2)=dim( W_1)+dim( W_2)-dim( W_1n W_2).

    2. Let W_1 and W_2 be finite-dimensional subspaces of a vector space V, and let V= W_1+ W_2. deduce that V is the direct sum of W_1 and W_2 iff dim(V)=dim( W_1)+dim( W_2)
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  2. #2
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    Quote Originally Posted by studentmath92 View Post
    1. Prove that if W_1 and W_2 are finite-dimensional subspaces of a vector space V, then the subspace W_1+ W_2 is finite-dimensional and dim( W_1+ W_2)=dim( W_1)+dim( W_2)-dim( W_1n W_2).

    2. Let W_1 and W_2 be finite-dimensional subspaces of a vector space V, and let V= W_1+ W_2. deduce that V is the direct sum of W_1 and W_2 iff dim(V)=dim( W_1)+dim( W_2)
    These are results that should be available in most of the std texts. Where are you getting stuck?
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