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Math Help - Subspaces take 2.

  1. #1
    Super Member Showcase_22's Avatar
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    Subspaces take 2.

    Let V=\mathbb{R}^4. Suppose further that W_1 is a subsapce of V spanned by vectors (1,2,0,1) and (1,1,1,0), and  W_2 is a subspace of V spanned by (2,3,1,1).

    Determine dim(W_1+W_2) and dim(W_1 \cap W_2).
    My other thread might be useful: http://www.mathhelpforum.com/math-he...subspaces.html

    Sifting (1,2,0,1) and (1,1,1,0) gives those two vectors. Hence dim(W_1)=2.

    Similarly dim(W_2)=1.

    Since (1,2,0,1)+(1,1,1,0)=(2,3,1,1) we know that W_2 is a subspace of W_1.

    Therefore dim(W_1 \cap W_2)=1 and dim(W_1+W_2)=2.

    Is this it? This question was worth 10 marks but my answer is remarkably small!
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  2. #2
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    Quote Originally Posted by Showcase_22 View Post
    My other thread might be useful: http://www.mathhelpforum.com/math-he...subspaces.html

    Sifting (1,2,0,1) and (1,1,1,0) gives those two vectors. Hence dim(W_1)=2.

    Similarly dim(W_2)=1.

    Since (1,2,0,1)+(1,1,1,0)=(2,3,1,1) we know that W_2 is a subspace of W_1.

    Therefore dim(W_1 \cap W_2)=1 and dim(W_1+W_2)=2.

    Is this it? This question was worth 10 marks but my answer is remarkably small!
    your solution is correct.
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  3. #3
    Super Member Showcase_22's Avatar
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    your solution is correct.
    nifty!

    If you were doing this question, would you add in anything else?

    It seems a little small for 10 marks!
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