Vector spaces

[Filip84]

Hi,

can somebody help me with the following problems:

*5. An n-dimensional vector space over the field of complex scalars is isomorphic to the vector space of n-tuples of complex numbers. If m vectors are given with m < n, state a test for linear dependence in terms of the rank of an n-by-m matrix formed by using the m n-tuples as columns. What happens in the case m > n?
*6. Prove that in an n-dimensional vector space any set of n+1 vectors is linearly dependent.

Thank you.

 

[HallsofIvy]

What, exactly, is your difficulty? Do you not know the definitions of the words "independent" and "dependent" for sets of vectors? That is what these problems depend on.

 

[Filip84]

What, exactly, is your difficulty? Do you not know the definitions of the words "independent" and "dependent" for sets of vectors? That is what these problems depend on.

Yes, i know the definitions of the words "independent" and "dependent". I dont know how to formulate these proofs.

Thanks