# Prove that there does not exist a linear map from ...

Prove that there does not exist a linear map from F

{(x

^{5}to F^{2}whose null spaceequals{(x

_{1},x_{2},x_{3},x_{4},x_{5})F^{5}:x_{1}= 3x_{2}and x_{3}= x_{4}=x_{5}}.Comments

## Answers ( 1 )

^{5}to F^{2}.^{2}= 2.^{5}= 5._{1},x_{2},x_{3},x_{4},x_{5}only two are independent. so the dim of null space of T can bemaximum 2.^{5}dim of range of T + dim of null space ofT.^{5}to F^{2}.