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Math Help - Determine if the given vectors span R4

  1. #1
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    Determine if the given vectors span R4

    In each case determine if the given vectors span R4. Support your answer.
    {[1 1 1 1], [0 1 1 1], [0 0 1 1], [0 0 0 1]}.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    One way: express:

    (x_1,x_2,x_3,x_4)=\lambda_1(1,1,1,1)+\ldots+\lambd  a_4(0,0,0,1)\quad (*)

    and prove that for all (x_1,\ldots,x_4) the system (*) has solution on the unknowns \lambda_1,\ldots,\lambda_4 .


    Fernando Revilla
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Another (simpler) way: Let the given vectors be v_1, v_2, v_3, v_4.

    \{v_1-v_2,v_2-v_3,v_3-v_4,v_4\}=\{(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1  )\}, which is the standard basis in R^4.
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