# Matrix of Linear Transformation

• Dec 5th 2009, 12:29 PM
RB06
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
• Dec 5th 2009, 12:36 PM
lvleph
So are you saying that $f(t) = \begin{pmatrix}1 & 0 & 0 \\ 0 & t & 0 \\ 0 & 0 & t^2\end{pmatrix}$?
• Dec 6th 2009, 03:24 AM
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.
• Dec 6th 2009, 08:12 AM
lvleph
Quote:

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 $P_2$.