Can a Set of 5 Vectors Span All of R6?

[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.

 

[Dick]

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

 

[ykaire]

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

I'm not sure, to be honest.

 

[venom192]

How many vectors span R2? R3?

 

[ykaire]

How many vectors span R2? R3?

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

 

[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?