Matrix of Linear Transformation

**RB06** · December 5th 2009, 11:29 AM

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

**lvleph** · December 5th 2009, 11:36 AM

So are you saying that $f(t) = \begin{pmatrix}1 & 0 & 0 \\ 0 & t & 0 \\ 0 & 0 & t^2\end{pmatrix}$ ?

**Shanks** · December 6th 2009, 02:24 AM

$P_3$ 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.

**lvleph** · December 6th 2009, 07:12 AM

Originally Posted by Shanks

$P_3$ 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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