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Math Help - basis spanning R4

  1. #1
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    basis spanning R4

    hi,

    given two vectors:

    v_1=\left[\begin{array}{cc}1\\1\\1\\1\end{array}\right]

    and

    v_2=\left[\begin{array}{cc}1\\2\\3\\4\end{array}\right]

    i need to come up with two more vectors (eg U_1 and U_2) which when in a set with the first two create a basis for R^4. i tried using like a1,b1,c1,d1 for each u_1 and U_2 and getting it into REF but i had no joy. apparently according to my friend you should be able just to guess the vectors which satisfy this.

    thanks,
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Adding for example v_3=(0,0,1,0)^t,v_4=(0,0,0,1)^t you'll get a rank 4 matrix, that is the columns are linearly inedependent. Now use that n linearly independent vectors in a vector space V of dimension n form a basis of V .
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