If V is a finite dimensional vector space and W



Answered question


If V is a finite dimensional vector space and W is a subspace, the W is finite dimensional. Prove it.

Answer & Explanation

David Clayton

David Clayton

Beginner2022-01-07Added 36 answers

By definition-
If V be a vector space over an arbitray field F, then we say that V is finite dimensional if it is spanmed by a finite set of vectors.
Let, dimV =n
V is spamed by a set of n linearly independent vectors in V,
say S={v1,v1,v1,...,vn}
Now, as W is a stubspace of then W is spaned by at most n elements of the set S.
Hence, by definition of finite dimensional vector sapace- W is finite dimensional.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?