If v is a nonzero vector in V,then there is exactly one linear transformation T: V -> W such that T(-v) = -T(v)
I believe this is true, however the solution manual said it was false. I proved by construction given that v1,v2,...,vn are the basis vectors for V, let T1, T2 be linear transformations such that T1 =/= T2. then by homogeneity, I got that T1(-v) = T2(-v), but that contradicts that T1,T2 are not equal therefore it is true.
There is exactly one linear transformation T: V -> W for which T(u+v) = T(u-v) for all vectors u and v in V.
I don't even know where to begin with this so any hints are much appreciated and welcome !