- #1
peripatein
- 880
- 0
Hi,
I wish to pose a few questions I have concerning transformations:
(1) I am trying to disprove the following statement:
Let T: V->U be a linear transformation between vector spaces V and U, and let {v1,...,vn} be a set of vectors in V.
If {Tv1,...,Tvn} spans U, then {v1,...,vn} spans V.
(2) I would like to find the kernel and image of the following linear transformation:
T:R2[x]->R2[x], T(p(x)) = xp(1) - xp'(1)
(1) I came up with the following counter example, which I am not sure is correct:
R2[x]->R2[x], T(p(x)) = int(p(x))dx
I'd appreciate some feedback on this counter example.
(2) I got that the ker(T) would have to be zero, and Im(T) = Sp{x,0,-x}. May someone kindly confirm please?
Homework Statement
I wish to pose a few questions I have concerning transformations:
(1) I am trying to disprove the following statement:
Let T: V->U be a linear transformation between vector spaces V and U, and let {v1,...,vn} be a set of vectors in V.
If {Tv1,...,Tvn} spans U, then {v1,...,vn} spans V.
(2) I would like to find the kernel and image of the following linear transformation:
T:R2[x]->R2[x], T(p(x)) = xp(1) - xp'(1)
Homework Equations
The Attempt at a Solution
(1) I came up with the following counter example, which I am not sure is correct:
R2[x]->R2[x], T(p(x)) = int(p(x))dx
I'd appreciate some feedback on this counter example.
(2) I got that the ker(T) would have to be zero, and Im(T) = Sp{x,0,-x}. May someone kindly confirm please?