Question

Linear Algebra concept question: For a vector space of n>0, is it possible for a set of n-1 linearly independent vectors to span it?

Answer 1

My gut says no. but, I'm not too sure why and not having much luck finding anything that explicitly states that.
But this would basically mean that in order for a subspace say, U to span a vector space, say V, then this would mean dim(U) =dim(V), or in other words, if dim(V) = 3, U must contain 3 linearly independent vectors if it is going to be a spanning set of V. Is this correct?