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Math Help - Direct Sum of two Subspaces

  1. #1
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    Direct Sum of two Subspaces

    let U be subspace of R^4 spanned by the vectors
    u_1=(1,-2,5,-3),u_2=(2,3,1,-4),u_3=(3,8,-3,-5)

    the vectors v_1=(1,-2,5,-3),v_2(0,7,-9,2) form basis for the Subspace U. and v_1,v_2,v_3=(0,0,1,0),v_4=(0,0,0,1) form basis for R^4. How do i find the subspace W of R^4 such that R^4=U \oplus W

    Thanks for any help.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by charikaar View Post
    let U be subspace of R^4 spanned by the vectors
    u_1=(1,-2,5,-3),u_2=(2,3,1,-4),u_3=(3,8,-3,-5)

    the vectors v_1=(1,-2,5,-3),v_2(0,7,-9,2) form basis for the Subspace U. and v_1,v_2,v_3=(0,0,1,0),v_4=(0,0,0,1) form basis for R^4. How do i find the subspace W of R^4 such that R^4=U \oplus W

    Thanks for any help.
    Hint: think orthogonal complement.
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  3. #3
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    Still can't go ahead. anymore help/hints please?
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