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Math Help - Prove that the set is not a subspace of vector space

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    Prove that the set is not a subspace of vector space

    How can I verify that the following is not a subspace of the vector space with an example?

    W is the set of all linear functions ax+b, where are is not equal to 0, in C(-infiniti, infiniti)
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ephemeral1 View Post
    How can I verify that the following is not a subspace of the vector space with an example?

    W is the set of all linear functions ax+b, where are is not equal to 0, in C(-infiniti, infiniti)
    -ax+b+ax+b=2b\notin \left\{mx+n:m,n\in\mathbb{R}-\{0\}\right\}
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    Could you elaborate on your answer? I don't understand the last part of your answer. The one with R-{0}}. Thank you.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ephemeral1 View Post
    Could you elaborate on your answer? I don't understand the last part of your answer. The one with R-{0}}. Thank you.
    If you take x+1 and -x+1 they are both in the set. But, x+1+-x+1=2 is not since it's leading coefficient is zero.
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