Let $V$ be a vector space and $U$ be a subspace of $V$. Given a Linear transformation $T : V \to W$ between vector spaces $V$ and $W$ what is $Ker(T) \cap U$ ?
How would we find this? is it $\{0\}$ ?
Intersection of Kernel(T) and Subspace of Domain
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linear-algebra
vector-spaces
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0It would depend on what $T$ is. It's the kernel of $T$ restricted to $U$. It would also depend on $U$. – 2017-02-06
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0It could be anything, since every subspace of $V$ is the kernel of a linear transformation. – 2017-02-06