Is the Intersection of Subspaces a Subspace in a Vector Space?

[zhenghao1]

Hi to all,

I really need help fast.

How do I solve this question? A solution would be much appreciated. THANKS A MILLION!

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Let S1 and S2 be the two subspaces in a vector space V. Show that the intersection of S1 and S2 is also a subspace in V.
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[d_leet]

You need to show some work. What is the definition of a subspace?

 

[zhenghao1]

Question

Ok sorry, there was one piece of information that I left out.

The question is:

Let S1 and S2 be the two subspaces in a vector space V. Show that the intersection of S1 and S2 is also a subspace in V.

Assume vector space over GF(2).

Can someone please help me? Thanks!

 

[d_leet]

That doesn't change anything. You need to show us what you have attempted already? What is the definition of a subspace?

 

[andytoh]

Let a, b any two elements in the intersection and show that they satisfy the 3 rules of subspace. Any textbook should also have the proof already because this is a common theorem.