Proving Subspaces of Finite-Dimensional Vector Spaces

[hkus10]

1) How to show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional and dim W<= dimV.

2) How to show that if a subspace of a finite-dimensional vector space V and dim W = dimV, then W = V.

3) How to prove that the subspace of R^3 are{0}, R^3 itself, and any line or plane passing through the origin.

How to approach these three Questions?

Thanks

 

[HallsofIvy]

You approach any "proof" by looking at the definitions! What is the definition of "finite dimensional" vector space? What is the definition of "dimension" for such a space?