I want to show that Nullspace (normed space) is a vector space. can someone help

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I want to show that Nullspace (normed space) is a vector space. can someone help

Mathematics
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null spaces are defined reference to some linear transformation
yes. I mean a linear transformation on a normed vector space
so u want to show it a subspace?

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yes
the condition is, for x,y in space n a, b scalars ax+by must belong to the space...right?
i think so, if that is enough to show
\[x, y \in N\]
then \[T ( x )= T ( y ) = 0\]
T (ax + by) = a T(x) +bT(y) using the linarity
T (ax + by) = a T(x) +bT(y)=0 showing that ax + by is in N
so N is the vector subspace

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