Let L:p2 >>> p3 be the linear transformation defined by L(p(t)) = t^2 p'(t).(adsbygoogle = window.adsbygoogle || []).push({});

(a) Find a basis for and the dimension of ker(L).

(b) Find a basis for and the dimension of range(L).

The hint that I get is to begin by finding an explicit formula for L by determining

L(at^2 + bt + c).

Does this hint mean let p(t) = at^2 + bt + c?

Then, I find that t^2 p'(t) = 2at^3 + bt^2.

Then, I conclude that the basis for ker(L) = {1}.

Is it right?

Also, how to find range(L)?

Thanks

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# Kernal and Range of a Linear Transformation

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