Vector space/Dimension n and n vectors/Equivalences/Fact

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space with finite dimension ${}n=\dim _{}{\left(V\right)}$. Let ${}n$ vectors ${}v_{1},\ldots ,v_{n}$ in ${}V$ be given.

Then the following properties are equivalent.

1. ${}v_{1},\ldots ,v_{n}$ form a basis of ${}V$.
2. ${}v_{1},\ldots ,v_{n}$ form a generating system of ${}V$.
3. ${}v_{1},\ldots ,v_{n}$ are linearly independent.

Write a proof