Questions about vector spaces, matrices, and eigenvalues

Hiya, I'm a bit stuck and I need help answering these short questions:

- Suppose that (V,+,.) is a vector space over a field F & S= {V1,V2,...,Vk) is a subset of V. Describe the span of S. Explain how to determine whether S is linearly independant.

- Explain what it means for W to be a subspace of (V,+,.)

- What is meant by Y:V -> W is an F-linear transformation

- Defne what is meant by saying a matrix is diagonalisable, describe the connection wih the eigenvectors and eienvalues of the matrix.

- Let V denote a real vector space & B:VxV->**R **denote a real bilinear form of V. Describe what two additional properties B must satisfy in order to be an inner product on V

If you know the answers please help. I can't string together sentences to answer them.

Thanks, Steve