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Math Help - Showing basis for Field?

  1. #1
    Junior Member
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    Showing basis for Field?

    let F be a field. we have
    e1=(1 -1 1)
    e2=(0 1 1)
    e3=(1 0 1)
    and need to show that {e1, e2, e3} is a basis for F^3

    so far i've shown independence, but am stuck on the spanning bit.
    please note that F^3 is not the mod3 field

    thank you
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For every

    (x_1,x_2,x_3)\in \mathbb{F}^3

    express:

    (x_1,x_2,x_3)=\lambda_1(1,-1,1)+\lambda_2(0,1,1)+\lambda_3(1,0,1)

    and prove that the corresponding system has solution on \mathbb{F} for all x_1,x_2,x_3 .

    Regards.

    Fernando Revilla
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