Span in R6

1. Sep 6, 2012

ykaire

1. Can a set of 5 vectors in R6 span all of R6?

I want to say that it does span, because i remember my teacher saying "don't think of the physical world," but i'm not entirely sure if it does.

Last edited: Sep 6, 2012
2. Sep 6, 2012

Dick

Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?

3. Sep 6, 2012

ykaire

I'm not sure, to be honest.

4. Sep 6, 2012

venom192

How many vectors span R2? R3?

5. Sep 6, 2012

ykaire

Um, I'm guessing that vectors span R2 and 3 Vectors span R3.
so... that must mean that 6 vectors span R6.

Last edited: Sep 7, 2012
6. Sep 7, 2012

HallsofIvy

Why are you doing all of this guessing? It looks to me like you need to review the basic definitions. You should know immediately that R6 has dimension 6. What does that mean. What can you say about any spanning set in a space of dimension n? What can you say about any linearly independent set in a space of dimension n?