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Math Help - polynomials spanning P2

  1. #1
    Member Jskid's Avatar
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    polynomials spanning P2

    Does the folloowing set of polynomials span P_2?
    {t^2+2t-1, t^2-1}
    When I formed the coefficient matrix I got
    <br />
\left[ {\begin{array}{ccc}<br />
 1 & 1 & 0  \\<br />
 2 & 0 & 0  \\<br />
 -1 & 0 & 0 \\<br /> <br />
 \end{array} } \right]<br /> <br />

    but the answer key had
    <br />
\left[ {\begin{array}{cc}<br />
 1 & 1   \\<br />
 2 & 0   \\<br />
 -1 & 0  \\<br /> <br />
 \end{array} } \right]<br /> <br />
    Is one right/wrong or better?
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  2. #2
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    Quote Originally Posted by Jskid View Post
    Does the folloowing set of polynomials span P_2?
    {t^2+2t-1, t^2-1}
    When I formed the coefficient matrix I got
    <br />
\left[ {\begin{array}{ccc}<br />
 1 & 1 & 0  \\<br />
 2 & 0 & 0  \\<br />
 -1 & 0 & 0 \\<br /> <br />
 \end{array} } \right]<br /> <br />

    but the answer key had
    <br />
\left[ {\begin{array}{cc}<br />
 1 & 1   \\<br />
 2 & 0   \\<br />
 -1 & 0  \\<br /> <br />
 \end{array} } \right]<br /> <br />
    Is one right/wrong or better?

    What do you need any matrix for? The space P_2 is of dimension 3, and you're given only 2 vectors...

    Tonio
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  3. #3
    MHF Contributor

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    Where did that third column come from? You were given two vectors so the matrix should have two columns.
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