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Math Help - linear span

  1. #1
    Senior Member sfspitfire23's Avatar
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    linear span

    Hi guys,

    I'd like to know whether I'm thinking about this in the right way.

    Let's say that I have a subspace of R^4 and have found an orthonormal basis for it that consists of three vectors. If I want to then find a basis for all of R^4 i need to find a vector that is not in the same linear span as the original three vectors and perform Gram-Schmidt. This is the same as finding a vector that is not a linear combination of the original three vectors. So, I would put all four vectors into a matrix (as rows) and then put it into rref. If the matrix has no all-zero rows, the four vectors are linearly independent, and therefore the vector I choose is not in the linear span of the first three vectors and can be used to find a basis for all of R^4

    Thanks
    Last edited by sfspitfire23; October 23rd 2012 at 01:05 PM.
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  2. #2
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    israel
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    Re: linear span

    Yes,this is what you should do.
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  3. #3
    Member
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    Re: linear span

    Yes,this is what you should do.
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