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Math Help - Basis Matrix

  1. #1
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    Basis Matrix

    I was tutoring yesterday and I got caught completely offguard by this question:

    Let B= \{ 1+t^2,3-t+4t^2,-1+2t-4t^2 \}

    Find  [1-3t+5t^2]_B and find q such that [tex]q_B = (1,3,-2)

    I forgot most of my linear algebra, and I don't have my notes with me, would anyone please explain this to me? Thanks.
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  2. #2
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    You want, 1 - 3t + 5t^2 = a\left( {1 + t^2 } \right) + b\left( {3 - t + 4t^2 } \right) + c\left( {1 + 2t - 4t^2 } \right).
    So
    \begin{gathered}<br />
a + 3b + c = 1 \hfill \\<br />
- b + 2c = - 3 \hfill \\<br />
a + 4b - 4c = 5 \hfill \\ <br />
\end{gathered} <br />
    SOLVE!
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