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

this question was in a test the previous year:

Decide, whether this statement is right or not (in accord with the content of the lecture). Justify your decision:

LetVbe a vector space andUits subspace. Then, in some casesV \ Ucould be the subspace ofV, but generally it doesn't have to be a subspace ofV

I think thatV \ Ucan't be a subspace, because each subspace must fit this conditions:

[tex]

0 \in W

[/tex]

[tex]

a \in W, b \in W \rightarrow a + b \in W

[/tex]

[tex]

a \in \mathbb{K}, v \in W \rightarrow a.v \in W

[/tex]

So, ifUissubspace, it contains0. So,V \ Udoesn't contain0=> it isn't a subspace.

Is this a right conclusion?

Thank you.

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