Let $V=span\{ b_1, \ldots, b_n\}$ be a $n$-dimensional vector space. Defined on $V$ is a linear functional $\Lambda$. Let $$V_\Lambda:= \{x \in V: \Lambda(x) = 0 \}$$
How can I find a basis of $V_\Lambda$? The orthogonal projection from $P: V \to V_\Lambda$ would help, but in order to find the projection $P$ I need a basis of $V_\Lambda$, which is my original problem.
Thanks for any hints!