(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let (F2) ={0,1} denote the field with 2 elements.

i) Let V be a vector space over (F2) . Show that every non empty subset W of V which is closed under addition is a subspace of V.

ii) Write down all subsets of the vector space (F2)^2 over (F2) and underline those subsets which are subspaces.

2. Relevant equations

3. The attempt at a solution

For i.) do i need to show that it is closed under scalar multiplication also? I don't understand how it is because for example 6x1=6 which is not of F2??

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# Homework Help: Is it a subspace or not?

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