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Math Help - Subset and spanning

  1. #1
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    Subset and spanning

    * Determine whether H, a subset of the vector space V, is a subspace of V:
    a) V=M^n,n , H={A E M^n,n : det A does not =0}
    b) V=P3, H={p E P3 : p(0)=0}


    *If p1, p2,.....pm span Pn, write down a mathematical relationship between m and n.


    Any help is greatly appreciated!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jacko View Post
    * Determine whether H, a subset of the vector space V, is a subspace of V:
    a) V=M^n,n , H={A E M^n,n : det A does not =0}
     V is the space of all n \times n matrices.

     H is the subset of V of matrices with non-zero determinant.

    To be a subspace H must contain the zero matrix, but this has
    zero determinant, so is not in H so H is not a subspace.

    RonL
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  3. #3
    Grand Panjandrum
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    [quote=Jacko;68881b) V=P3, H={p E P3 : p(0)=0}
    [/quote]

    Please provide more explanation of you will leave us guessing at what your
    notation means

    RonL
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  4. #4
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    Thanks for your help!
    Sorry, the second part of the question is meant to read:
    * Determine whether H, a subset of the vector space V, is a subspace of V:

    V=P3 , H={p is an element of P3: p(0)=0}

    I hope thats more clear
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Jacko View Post
    Thanks for your help!
    Sorry, the second part of the question is meant to read:
    * Determine whether H, a subset of the vector space V, is a subspace of V:
    V=P3 , H={p is an element of P3: p(0)=0}

    I hope thats more clear
    If you said P3 is the space of polynomials of degree no grater than 3 that might help.

    RonL
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  6. #6
    Grand Panjandrum
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    I have closed this thread as OP has double posted the second question in a new thread and already has responses there.

    RonL
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