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Math Help - Matrix of Linear Transformation

  1. #1
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    Matrix of Linear Transformation

    I need help on the following:

    Find the matrix of the linear transformation  T(f(t)) = \int_{-6}^{7} f(t) dt from  P_3 to  \mathbb {R} with respect to the standard bases for  P_3 and  \mathbb {R} .

    Thanks
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  2. #2
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    So are you saying that f(t) = \begin{pmatrix}1 & 0 & 0 \\ 0 & t & 0 \\ 0 & 0 & t^2\end{pmatrix}?
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  3. #3
    Senior Member Shanks's Avatar
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    P_3 is the collection of polynomials with degree not greater than 3, it can be spanned by \{1, t, t^2, t^3\}.
    Calculate the integration as the image of the base in P_3, the matrix is a diagonal matrix whose diagonal elements are those image.
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  4. #4
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    Quote Originally Posted by Shanks View Post
    P_3 is the collection of polynomials with degree not greater than 3, it can be spanned by \{1, t, t^2, t^3\}.
    Calculate the integration as the image of the base in P_3, the matrix is a diagonal matrix whose diagonal elements are those image.
    You're right. I am not sure why I did P_2.
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