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, 201114 yr by hkus10

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).