Dick said:Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?
Um, I'm guessing that vectors span R2 and 3 Vectors span R3.venom192 said:How many vectors span R2? R3?
No, a set of 5 vectors cannot span all of R6. In order to span a vector space, the number of vectors in the set must be equal to or greater than the dimension of the vector space.
In order to span R6, at least 6 vectors are needed. This is because R6 is a 6-dimensional vector space.
Yes, a set of 5 linearly independent vectors can span all of R6. Linear independence means that none of the vectors in the set can be written as a linear combination of the other vectors in the set.
The maximum number of vectors needed to span R6 is 6. This is because R6 is a 6-dimensional vector space, so a set of 6 linearly independent vectors can span all of R6.
Yes, a set of 5 non-coplanar vectors can span all of R6. Coplanar vectors are those that lie in the same plane, so by having 5 non-coplanar vectors, we ensure that they span a 5-dimensional subspace of R6, which is all of R6.