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Math Help - Linear Spaces

  1. #1
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    Linear Spaces

    Find a basis of the linear space and thus determine the dimension.

    q(t) : q'(1)=q(2)

    Where q is a subset of Q_2: all polynomials of degree less than or equal to 2. I had to change it from p to q so the forum didn't make it a smiley...

    I'm not sure what to do here. I created an arbitrary form of q(t) and q'(t) and found a basis for each of these.

    q(t) = a+bt+ct^{2}
    \ss =(1,t,t^2)

    q'(t) = t+2ct
    \ss = (t)

    Now I'm lost, and I'm pretty certain I was never on the right track. Any help would be extremely appreciated.

    Thanks.
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  2. #2
    Senior Member Tinyboss's Avatar
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    You're on the right track. Your derivative should be b+2ct, not t+2ct. Evaluating q' and q at 1 and 2 respectively, you get b+2c = a+2b+4c. This is a linear system of three unknowns and one equation, so it's just basic linear algebra from here.
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  3. #3
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    Thanks, got it!

    Last edited by tangibleLime; May 3rd 2011 at 09:02 PM.
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