Vector Space and dim

[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

[DrRocket]

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

 

What have you tried ?

 

These should be pretty simple if you were paying attention in class.

 

D0 you know the definitions of: 1) linearly independent set, 2) spanning set, 3) basis, and 4) dimension ?