Ok. i have a problem that states: "suppose U and V are finite-dimensional vector spaces and that S [tex]\in[/tex] L(V,W), T [tex]\in[/tex] L(U,V). prove that(adsbygoogle = window.adsbygoogle || []).push({});

dim(null(ST))[tex]\leq[/tex] dim(null(S)) + dim(null(T)).

i think that some call the null space the kernel.

i have tried using the fact that null(S) is a subspace of V, null(T) is a subspace of U, and null(ST) is a subspace of U.

also, that:

dim(null(T)) [tex]\geq[/tex] dim(U) - dim(V)

dim(null(S)) [tex]\geq[/tex] dim(V) - dim(W)

dim(null(ST)) [tex]\geq[/tex] dim(U) - dim(W)

the closest that i get is that dim(null(ST))= dim(null(S)) + dim(null(T)).

Can anyone offer any suggestions?

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# Dim and null question

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