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Determine if the following is a linear transformation. If so, find the standard matrix of the transformation.

$T:P_1\to P_2$ such that $$T(p(t))= \int p(t) dt$$

I'd appreciate any help, an explanation of how to approach the problem would be extremely helpful. Thank you!

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    What are $P_1$ and $P_2$?2012-10-18
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    There are no specifications for P1 and P2. What is stated in the problem is all the information give for those two values.2012-10-18
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    Perhaps they are the spaces spanned by $\{1,x\}$ and $\{1,x,x^2\}$, respectively? Some books use that notation.2012-10-18
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    @Sharon The use of $p$ strongly suggests polynomials, as sourisse is noting. Moreover, if you're being asked for the standard matrix, you need finitely generated vector spaces.2012-10-18
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    I suspect it should be definite integral there.2012-10-18
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    Ok. Then after I find the vector spaces, I would perform the transformation on each space (i.e. take the integral of 1, x and x^2) to find the standard matrix?2012-10-18
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    @nikita2 it should not be a definite integral, if $T$ is supposed to take degree $1$ polynomials to degree $2$ ones. What you're thinking of would be a linear functional on $P_1$.2012-10-18
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    @Kevin, definite integral in the sense of $\int_0^t$.2012-10-18
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    Sharon, you find a basis $B$ for $P_1$, you find a basis $C$ for $P_2$, you apply $T$ to each element in $B$, you express each result in terms of $C$, you extract the coefficients of those expressions you have found, voila! there's your matrix.2012-10-18
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    Ooooh, sorry @nikita2, you're right.2012-10-18

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