Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I need some proofs for my assignment, the question is like below:

Let L be a linear map from the vector space V to the vector space W.

• ker(L) is a subset of V which consists of vectors u such that Lu = 0. Is ker(L) a

vector subspace of V ? Give a proof.

• Let S be a subset of V which consists of vectors which are not contained in ker(L).

Is S a vector subspace of V ? Give a proof.

• Let T be a subset of W which consists of vectors which are contained in Range L.

Is T a vector subspace of W? Give a proof.

• Let T be a subset of W which consists of vectors which are not contained in

Range L. Is T a vector subspace of W? Give a proof.

Thanks in advance

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# Homework Help: Linear Algebra, proof

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