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Math Help - Find the Basis of a row

  1. #1
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    Find the Basis of a row

    I just need the concept so on something simple like 1100 0111 0000 0000 Any help is greatly appreciated*Sorry, for some reason, I can't enter down. Bascially it is a 4x4 matrix while using those numbers
    Last edited by CollegeGal09; March 17th 2012 at 10:50 AM.
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  2. #2
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    Re: Find the Basis of a row

    "rows" don't have a basis, row SPACES do. rows are vectors. vector spaces have bases.

    in this case, each row can be regarded as an element of R^4. since 0-elements are always linearly dependent, only non-zero rows are eligible for membership in a basis. you have 2 non-zero row vectors:

    (1,1,0,0) and (0,1,1,1).

    to prove this is a basis for the row space, you need to show linear independence.

    so suppose a(1,1,0,0) + b(0,1,1,1) = (0,0,0,0). this is the same as saying:

    (a,a+b,b,b) = (0,0,0,0)

    can you prove that we HAVE to have a = 0, and b = 0 (hint: look at the first two coordinates of the vectors on each side of the equality).
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