# Linear transformation question

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• Apr 1st 2010, 03:24 PM
justin016
Linear transformation question
I am having problem with this question

T: P2 --->R^2 T(a+bx+cx^2)=(a,b)

Find the basis for the kernel T and basis for the image T

according to the text book Kernel = { T(v)= 0 }, so the kernel should look like

T (a+bx+cx^2)=(0,0)

how exactly do you find the basis?

As for the image, up to my understanding, is it the entire vector space of P2 map into a subspace of R^2?
• Apr 1st 2010, 03:27 PM
Drexel28
Quote:

Originally Posted by justin016
I am having problem with this question

T: P2 --->R^2 T(a+bx+cx^2)=(a,b)

Find the basis for the kernel T and basis for the image T

according to the text book Kernel = { T(v)= 0 }, so the kernel should look like

T (a+bx+cx^2)=(0,0)

how exactly do you find the basis?

As for the image, up to my understanding, is it the entire vector space of P2 map into a subspace of R^2?

Come on. Let $(a,b)\in\mathbb{R}^2$ be arbitrary.What is $T(a+bx)$? Also, $T(a+bx+cx^2)=(a,b)=0\implies a=b=0$