Re: a question about vector subspaces

In article <14241598.1126033480368.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
woodland <woodland_56@xxxxxxxxx> wrote:

>i have a small question from linear algebra.
>let's say W is subspace of V, and let's define a coset
>{v}+W, where v belongs to V, so {v} +W = { v+w: w belongs to
>W}

>i have to prove that {v}+W is subspace of V iff v also belongs to W, where v could be any vector from V.

I don't see any question, large or small...

I assume your question is "How do I do that?"

Well, first you should show that if {v}+W is a subspace, then v
belongs to W. Then show that if v belongs to W, then {v}+W is a
subspace.

Hints: for the first implication, remember what vector MUST be
included in any subspace. For the second implication, remember that
every vector space must be closed under vector addition.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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