# Thread: Show that B' is a basis

1. ## Show that B' is a basis

Hello,

I was wondering, is it sufficient to prove that B' is a basis if I showed that B' is linearly independent?

Or do is there anything else I would have to do?

2. It needs to be a spanning set also.

3. Originally Posted by l flipboi l
I was wondering, is it sufficient to prove that B' is a basis if I showed that B' is linearly independent?
If $B'\subset V$ has $n$ elements and $\dim V=n$ , then

$B'\textrm{\;lin.\;indep.\;}\Rightarrow B' \textrm{\;basis\;of\;}V$

Regards.

Fernando Revilla