## anonymous 5 years ago I want to show that Nullspace (normed space) is a vector space. can someone help

1. anonymous

null spaces are defined reference to some linear transformation

2. anonymous

yes. I mean a linear transformation on a normed vector space

3. anonymous

so u want to show it a subspace?

4. anonymous

yes

5. anonymous

the condition is, for x,y in space n a, b scalars ax+by must belong to the space...right?

6. anonymous

i think so, if that is enough to show

7. anonymous

$x, y \in N$

8. anonymous

then $T ( x )= T ( y ) = 0$

9. anonymous

T (ax + by) = a T(x) +bT(y) using the linarity

10. anonymous

T (ax + by) = a T(x) +bT(y)=0 showing that ax + by is in N

11. anonymous

so N is the vector subspace