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war485
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Homework Statement
T: P2 --> P2 be a linear transformation defined by T(p(x)) = xp'(x)
where ' is the derivative
Describe the kernal and range of T and are any of the following polynomials in the range and or in the kernal of T?
2
x2
1 - x
Homework Equations
power rule (for derivatives)
The Attempt at a Solution
I took an arbitrary a+bx+cx2 and turned it into bx + 2cx2 after applying T on it. I understand that the kernal means some vector that will turn it into the zero vector (like finding its null). so does that b = c = 0 in order for this to work? Then will it imply that the kernal of T is the set of all constant polynomials? If this is right, then from this I think x2 and 2 and 1 - x should be in ker(T).
As for the range of T, I think it is all of P2, so that includes the 2, x2 and 1 - x.
Is all of what I've just done correct? I like checking my work here when I get stuck, you guys are so nice and great at helping people! :)