I'm stuck with the problem:
1. does a linear transformations (T:R3 to R3) exists that follwing these terms:
T(1,0,1)=T(2,1,2)=T(0,1,1)=T(2,3,3)
if there is give an example for such transformation, if not explain why?

2. Let V,W be vector spaces over the same field, both from a finite dimension.
Let U sub space of V and dimU>=dimv-dimw
prove that there is a transformation T:V to W, that sustains kerT = U.

Thanks ahead