16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.3.10

Vector Spaces

Mathematics — Linear Algebra · finite-dimensional-from-spanning-set

Problem

Let

V

be a vector space over the field

F

. Suppose there are a finite number of vectors

\alpha_1, \ldots, \alpha_r

V

which span

V

. Prove that

V

is finite-dimensional.