- #1
hkus10
- 50
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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.
Then, I conclude that the basis for ker(L) = {1}.
Is it right?
Also, how to find range(L)?
Thanks
(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