Proving that W1 \cap W2 is a Subspace of V

[mandygirl22]

Prove that if W₁ and W₂ are subspaces of the vector space V, then W₁ $$\cap$$ W₂ is also a subspace of V.

Attempt at solution:
I really don't even know where to start on this because I am confused about how to prove in general that something is a subspace. Also, I don't know how to find what W₁ $$\cap$$ W₂ is. Please help!

 

[Mark44]

Prove that if W₁ and W₂ are subspaces of the vector space V, then W₁ $$\cap$$ W₂ is also a subspace of V.

Attempt at solution:
I really don't even know where to start on this because I am confused about how to prove in general that something is a subspace. Also, I don't know how to find what W₁ $$\cap$$ W₂ is. Please help!

W₁ $\cap$ W₂ consists of all the vectors that are in W₁ and in W₂.

To make it simpler to write, let's W = W₁ $\cap$ W₂.

What are the things you need to check to verify that a set is a subspace of a given vector space?