Question

If K a field, V a K-vectorspace and \[l1,l2 \in V*\], so that for all \[v \in V\] \[l1(v).l2(v) =0.\]

Proof that either \[l1 = 0\] or \[l2=0\]

Answer 1

Use a proof by contradiction. Show the general for of the inner product, and assume that both vectors are non-zero.