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Math Help - subspace and spanning

  1. #1
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    subspace and spanning

    In each case determine whether U is a subspace of R3. Support your answer.

    U={[r s t] | r,s, and t in R, -r+3s+2t=0}.
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  2. #2
    Senior Member Tinyboss's Avatar
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    f(r,s,t)=(-r+3s+2t) is a linear map (from R^3 to R), so its kernel (U) is a subspace of the domain.
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  3. #3
    MHF Contributor

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    Or just show that the set is closed under addition and scalar multiplication.

    If [r, s, t] is in that set then -r+3s+2t=0. If [u, v, w] is in that set, then -r+ 3v+ 2w= 0.

    What about [r+ u, s+ v, t+ w]? Does it satisfy that equation?

    What about [ar, as, at] for some number a? Does it satisfy that equation?
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