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Math Help - confused about finding another vector to form a basis

  1. #1
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    confused about finding another vector to form a basis

    I got a basis of kernel of a 2*4 matrix :

    (-5,1,-3,0)^{T}, (10,0,7,1)^{T}

    now, i found a vector:
     (0,2,1,1)^{T}
    how can i find another vector together with this form a basis of kernel?
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  2. #2
    Member
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    This is basis transformation issue.


    v1=(-5,1,-3,0)^{T}, v2=(10,0,7,1)^{T}
    w1=[v1 v2][2 1]^{T}
    example:
    w2=[v1 v2][1 1]^{T}, or [v1 v2][1 2]^{T}

    If [w1 w2]=[v1 v2]A, matrix A must be invertible
    w2 = [5 1 4 1] or [15 1 11 2]
    Last edited by math2009; February 9th 2009 at 05:16 PM.
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