Let be a Finitely Generated Vector Space, with Spanning Set . Let .
From the Steinitz Exchange Lemma, by contrapositive, we have that implies that is Linearly Dependent (assuming is a spanning set as hypothesis).
Let be a Finitely Generated Vector Space, with Spanning Set . Let .
From the Steinitz Exchange Lemma, by contrapositive, we have that implies that is Linearly Dependent (assuming is a spanning set as hypothesis).