# Matrix of Linear Transformation

• Dec 5th 2009, 11:29 AM
RB06
Matrix of Linear Transformation
I need help on the following:

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

Thanks
• Dec 5th 2009, 11:36 AM
lvleph
So are you saying that $\displaystyle f(t) = \begin{pmatrix}1 & 0 & 0 \\ 0 & t & 0 \\ 0 & 0 & t^2\end{pmatrix}$?
• Dec 6th 2009, 02:24 AM
Shanks
$\displaystyle P_3$ is the collection of polynomials with degree not greater than 3, it can be spanned by $\displaystyle \{1, t, t^2, t^3\}$.
Calculate the integration as the image of the base in $\displaystyle P_3$, the matrix is a diagonal matrix whose diagonal elements are those image.
• Dec 6th 2009, 07:12 AM
lvleph
Quote:

Originally Posted by Shanks
$\displaystyle P_3$ is the collection of polynomials with degree not greater than 3, it can be spanned by $\displaystyle \{1, t, t^2, t^3\}$.
Calculate the integration as the image of the base in $\displaystyle P_3$, the matrix is a diagonal matrix whose diagonal elements are those image.

You're right. I am not sure why I did $\displaystyle P_2$.