hkus10 Posted April 21, 2011 Share Posted April 21, 2011 (edited) Let L:p2 >>> p3 be the linear transformation defined by L(p(t)) = t^2 p'(t). (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. is the basis for ker(L) {t, 1} and the basis for range(L) {t^3, t^2}? Thanks Edited April 22, 2011 by hkus10 Link to comment Share on other sites More sharing options...

DrRocket Posted April 22, 2011 Share Posted April 22, 2011 Let L:p2 >>> p3 be the linear transformation defined by L(p(t)) = t^2 p'(t). (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. is the basis for ker(L) {t, 1} and the basis for range(L) {t^3, t^2}? Thanks Take a look at the definition of "keernel". Then see if you still think that {t,1} is a basis for ker(L). Link to comment Share on other sites More sharing options...

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