Finite field/Vectors/Generating system/Exercise

Let ${}K$ be a finite field with ${}q$ elements, and let ${}V$ be an ${}n$-dimensional vector space. Let ${}v_{1},v_{2},v_{3},\ldots$ be an enumeration (without repetitions) of the elements from ${}V$. After how many elements can we be sure that these form a generating system

of ${}V$.

Create a solution