sorry it's me again!
Let $V$ be a $\mathbb K$ vector space with finite basis $B$ and $M \subset V$ is a finite linear independent subset.
Show that a subset $A \subset B$ exists, so that $(B \backslash A) \cup M$ is a basis from $V$.
Can I cheat and use the subset $\{\}$ from $B$? This would get me $B \cup M$, which should be a basis from V. Or did I get everything wrong? It's weird, because apparently my colleagues used linear span to show this.
Thanks a lot again!